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Let G be a planar graph with maximum degree @D(G). We use @g"l^'(G) and @g"l^''(G) to denote the list edge chromatic number and list total chromatic number of G, respectively. In this paper, it is proved that @g"l^'(G)=@D(G) and @g"l^''(G)=@D(G)+1 if @D(G)>=6 and G has neither C"4 nor C"6, or @D(G)>=7 and G has neither C"5 nor C"6, where C"k is a cycle of length k.

A (g, f)-factor F of a graph G is called a Hamiltonian (g, f)-factor if F contains a Hamiltonian cycle. For a subset X of V(G), let N G (X)= gcup x∈X N G (x). The binding number of G is defined by bind(G)=min{| N G (X) |/| X|| ∅≠X⊂V(G), N G (X)≠V(G)}. Let G be a connected graph of order n, 3≤a≤b be integers, and b≥4. Let g, f be positive integer-valued functions defined on V(G), such that a≤g(x)≤f(x)≤b for every x∈V(G). Suppose n≥(a+b−4)2/(a−2) and f(V(G)) is even, we shall prove that if bind(G)>((a+b−4)(n−1))/((a−2)n−(5/2)(a+b−4)) and for any independent set X⊂V(G), N G (X)≥((b−3)n+(2a+2b−9)| X|)/(a+b−5), then G has a Hamiltonian (g, f)-factor.

Let G be a planar graph with maximum degree Δ. It is proved that if Δ ≥ 8 and G is free of k-cycles for some k ∈ {5,6}, then the total chromatic number χ′′(G) of G is Δ + 1.

Let G(V, E) be a simple graph, and let f be an integer function on V with 1 ≤ f(v) ≤ d(v) to each vertex v e V. An f-edge cover-coloring of a graph G is a coloring of edge set E such that each color appears at each vertex v e V at least f(v) times. The f-edge cover chromatic index of G, denoted by χ′fc(G), is the maximum number of colors such that an f-edge cover-coloring of G exists. Any simple graph G has an f-edge cover chromatic index equal to δf or δf - 1, where δf= minv e V{⌊ d(v)/f(v)⌋} Let G be a connected and not complete graph with χ′fc(G) =δf-1, if for each u, v e V and e = uv ∉ E, we have χ′fc(G + e) > χ′fc(G) then G is called an f-edge covered critical graph. In this paper, some properties on f-edge covered critical graph are discussed. It is proved that if G is an f-edge covered critical graph, then for each u, v e V and e = uv ∉ E there exists w e {u,v} with d(w) ≤ δf(f(w)+1) -2 such that w is adjacent to at least d(w) - δf + 1 vertices which are all δf-vertex in G.

Introduction: Ischemia/reperfusion injury (IRI) may have deleterious consequences for donor heart. The underlying mechanisms involve inflammation that may culminate in primary or chronic graft failure. Hypothesis: Donepezil, an acetylcholinesterase inhibitor, can protect the post-transplanted donor heart by inhibiting systemic inflammation of the recipients. Methods: Here, we report in Lewis to Lewis rat syngenic heart transplantation model that ischemia/reperfusion injury resulted in primary and chronic graft failure that was prevented by recipient treatment with peroral single-dose Donepezil. Results: Donepezil inhibited the release of cytokines (TNF, IL-1β, IL-6 and IL18), CD11b/18 positive cell infiltration and myocardial apoptosis in the recipient rats one week postoperatively. One month after transplantation, the graft survival rate in Donepezil group was 46.7% than that in SHAM group (P Conclusions: Our results reveal that recipient treatment with Donepezil protects donor hearts through TNF inhibition and TNF related downstream pathophysiological pathways. These results suggest a novel, clinically feasible strategy to protect donor hearts from IRI.

Cardiocyte apoptosis plays an important role in the pathogenesis of heart diseases. The mechanism is unclear. It is reported that prolactin (PRL) is involved in cardiac disorders. This study aims to investigate the role of PRL in mediating the psychological stress-induced fibrofatty cell differentiation in the heart. In this study, BALB/c mice were treated with a 30-day restraint stress. The heart tissue was processed by paraffin embedding and hematoxylin and eosin. The expression of Sca1 in NIH3T3 cells was assessed by cell culture, flow cytometry and Western blotting. The results showed that chronic stress induced fibrofatty cells in the mouse heart and high serum PRL levels. The induction of fibrofatty cell was mimicked by administration with recombinant PRL. The stress also induced the expression of Sca1 in the mouse heart. Exposure of NIH3T3 cells (a fibroblast cell line) to PRL in the culture enhanced the expression of stem cell antigen-1 (Sca1), phosphorylation of signal transducer and activator of transcription 3 (STAT3) and expression of adipocyte-related protein molecules, including adiponectin, fatty acid binding protein (aP2), peroxisome proliferator activated receptor-g (PPARg) and CCAAT/enhancer binding protein (C/EBP)α, in the cells. We conclude that psychological stress-derived PRL induces fibroblasts to differentiate into fibrofatty cells in the heart.

To probe into the influence of transplantation of allogenic bone marrow mononuclear cells (BM-MNCs) on the left ventricular remodeling of rat after acute myocardial infarction (AMI), 60 male Wistar rats were evenly divided into three groups at random: control group 1, control group 2 and transplantation group. In control group 1, chest was opened without ligation of coronary artery; in control group 2 and transplantation group, the left anterior descending branch of coronary artery was ligated to establish AMI model. Prepared culture medium and allogenic BM-MNCs suspension were respectively implanted the surrounding area of infarcted cardiac muscle via epicardium of control group 2 and transplantation group. Four weeks after the operation, the osteopontin gene (OPN mRNA, P0.01), type I collagen (P0.01) and angiotensin II (AngII, P0.01) content in the left ventricular non-infarcted myocardium, and the Ang II density in blood plasma (P0.05) of transplantation group and control group 2 were all significantly higher than that of control group 1. In the transplantation group, the myocardial OPN mRNA, type I collagen and Ang II content of non-infarcted zone in left ventricle, and the Ang II concentration in blood plasma were all significantly lower than those of control group 2 (P0.05 for all). It is concluded that allogenic BM-MNCs transplantation may ease left ventricular remodeling after AMI by inhibiting the synthesis of type I collagen in the cardiac muscle and down-regulating the expression of Ang II and OPN gene.

Let G be a planar graph with maximum degree Δ such that G has no cycle of length from 4 to k, where k ≥ 4. Then the list chromatic index χ′1(G) = Δ and the list total chromatic number χ″1(G) = Δ + 1 if (Δ, k) ∈ {(7, 4), (6, 5), (5, 8)}. Furthermore, χ′1(G) = Δ if (Δ, k) ∈ {(4, 14)}.

The inner and outer layers of a turbulent channel flow over a superhydrophobic surface (SHS) are characterized using simultaneous long-range microscopic particle tracking velocimetry (micro-PTV) and particle image velocimetry, respectively. The channel flow is operated at a low Reynolds number of ReH = 4400 (based on full channel height and 0.174 m/s bulk velocity), equivalent to Reτ = 140 (based on half channel height and friction velocity). The SHS is produced by spray coating, and the root-mean-square of wall roughness normalized by wall-unit is k+rms = 0.11. The micro-PTV shows 0.023 m/s slip velocity over the SHS (about 13% of the bulk velocity), which corresponds to a slip-length of ∼200 μm. A drag reduction of ∼19% based on the slope of the linear viscous sublayer and 22% based on an analytical expression of Rastegari and Akhavan [J. Fluid Mech. 773, R4 (2015)] realized. The reduced Reτ over the SHS based on the corresponding friction velocity is ∼125, which is in the lower limit of a turbulence re...

One of the most important indicators of myocardial regeneration is cardiomyocyte proliferation. However, it is difficult to distinguish cardiomyocytes in the regenerating stage from binucleated or multinucleated myocytes by conventional morphometric techniques. As cell cycle progression (CCP) scores have been successfully applied to the evaluation of the proliferation of cancer cells, we sought to establish a multi-gene score to evaluate cardiomyocyte proliferation in this study. Given the disturbances of nuclear division without cell division that occurs in cardiomyocytes, ten cytokinesis-correlated genes (Anln, Aurkb, Cenpa, Kif4, Kif23, Prc1, RhoA, Spin1, TACC2, and CDC42) were chosen to establish the cardiomyocyte cytokinesis score (CC-Score). The expression levels of these genes in H9C2 rat cardiomyoblast cells, the proliferation of which were stimulated or inhibited, were detected using qRT-PCR. To confirm the feasibility of the CC-Score system, four conventional methods for evaluating cardiomyocyte proliferation, including the MTT assay, BrdU assay, immunofluorescence, and flow cytometry analysis, were used in each group. The results of the CC-Score in the assessment of the proliferation of H9C2 cells were consistent with those of four commonly used proliferative assay methods. We conclude that the CC-Score can be used to assess the proliferation status of H9C2 cells, and suggest that the CC-Score may be a potential method for the assessment of cardiomyocyte proliferation in myocardial regeneration. However, validation studies utilizing primary cultured rat cardiomyocytes and heart tissue are warranted.

One of the most important indicators of myocardial regeneration is cardiomyocyte proliferation. However, it is difficult to distinguish cardiomyocytes in the regenerating stage from binucleated or multinucleated myocytes by conventional morphometric techniques. As cell cycle progression (CCP) scores have been successfully applied to the evaluation of the proliferation of cancer cells, we sought to establish a multi-gene score to evaluate cardiomyocyte proliferation in this study. Given the disturbances of nuclear division without cell division that occurs in cardiomyocytes, ten cytokinesis-correlated genes (Anln, Aurkb, Cenpa, Kif4, Kif23, Prc1, RhoA, Spin1, TACC2, and CDC42) were chosen to establish the cardiomyocyte cytokinesis score (CC-Score). The expression levels of these genes in H9C2 rat cardiomyoblast cells, the proliferation of which were stimulated or inhibited, were detected using qRT-PCR. To confirm the feasibility of the CC-Score system, four conventional methods for evaluating cardiomyocyte proliferation, including the MTT assay, BrdU assay, immunofluorescence, and flow cytometry analysis, were used in each group. The results of the CC-Score in the assessment of the proliferation of H9C2 cells were consistent with those of four commonly used proliferative assay methods. We conclude that the CC-Score can be used to assess the proliferation status of H9C2 cells, and suggest that the CC-Score may be a potential method for the assessment of cardiomyocyte proliferation in myocardial regeneration. However, validation studies utilizing primary cultured rat cardiomyocytes and heart tissue are warranted.

The amnE gene from Pseudomonas sp. AP-3 has been verified as encoding a deaminase with 142 amino-acid residues. In order to change the substrate specificity via structure-based protein engineering, the amnE gene, after gene-code optimization, was chemically synthesized and cloned into the expression vector pET-28a. The protein was expressed in Escherichia coli BL21 (DE3) and purified by Ni(2+)-chelating affinity chromatography. Diffraction-quality crystals were obtained using the hanging-drop vapour-diffusion method and diffracted to a resolution of 2.09 Å. The crystals belonged to the orthorhombic space group C2221, with unit-cell parameters a = 63.23, b = 88.93, c = 137.83 Å.

The enhanced proliferation of mesenchymal stem cells (MSCs) can be helpful for the clinical translation of cell therapy. Low-level laser irradiation (LLLI) has been demonstrated as regulating MSC proliferation. MicroRNAs (miRNAs) are involved in various pathophysiologic processes in stem cells, but the role of miRNAs in the LLLI-based promotion of MSC proliferation remains unclear. We found that the proliferation level and cell cycle-associated genes in MSCs were increased after LLLI treatment in a time-dependent manner. Microarray assays revealed subsets of miRNAs to be differentially regulated, and these dynamic changes were confirmed by quantitative real-time polymerase chain reaction (qRT-PCR) after LLLI. miR-193 was the most highly up-regulated miRNA, and the change in it was related with the proliferation level. Gain-loss function experiments demonstrated that miR-193 could regulate the proliferation of MSCs, including human's and rat's, but could not affect the apoptosis and differentiation level. Blockade of miR-193 repressed the MSC proliferation induced by LLLI. By qRT-PCR, we found that miR-193, in particular, regulated cyclin-dependent kinase 2 (CDK2) expression. Bioinformatic analyses and luciferase reporter assays revealed that inhibitor of growth family, member 5 (ING5) could be the best target of miR-193 to functionally regulate proliferation and CDK2 activity, and the mRNA and protein level of ING5 was regulated by miR-193. Furthermore, the ING5 inhibited by small interfering RNA (siRNA) could up-regulate the proliferation of MSCs and the expression of CDK2. Taken together, these results strongly suggest that miR-193 plays a critical part in MSC proliferation in response to LLLI stimulation, which is potentially amenable to therapeutic manipulation for clinical application.

Lysophospholipids (LPs) are small signaling lipids that regulate diverse physiological and pathological processes through G protein-coupled receptors. To investigate the function of LP signaling in heart organogenesis and maturation, we measured the expression of 10 confirmed LP receptors (Lpar1–5 and S1pr1–5) in rat heart from embryonic day 19.5 (E19.5d) to postnatal week 12 (P12w). The expression of Lpar3 mRNA peaked at 37-fold higher than adult expression at P1d, while the expression levels of Lpar1 and Lpar4 increased markedly after P1d and peaked at 19- and 48-folds of adult expression on P7d. The expression levels of all three receptor mRNAs were significantly reduced by P21d and remained low thereafter. Expression of the corresponding receptor proteins also peaked during the early postnatal period but the subsequent decline was less dramatic from P14d to P12w compared to mRNA expression. In contrast, S1pr1 and S1pr3 exhibited more gradual developmental changes. Although early expression was higher than mature expression (3- to 6-fold), these receptors were still strongly expressed at P12w. The other isotypes examined, Lpar2, Lpar5, S1pr4, and S1pr5, were very weakly expressed at all developmental stages. Analysis of receptor distribution within the developing heart (P1d) revealed that Lpar1, Lpar3, and Lpar4 were expressed in the myocardium of all four chambers but not in valves, while Lpar3 was also uniquely expressed in the aorta and coronary vessels. Western blots revealed that the developmental changes in Lpar1, Lpar3, and Lpar4 protein expression mirrored changes in β-actin and β-tubulin expression. The increase in Lpar1 and Lpar4 receptors from P1d to P7d corresponds to the period of rapid myocardial growth and functional maturation. Moreover, the relatively high expression of Lpar1, Lpar3, and Lpar4 in the late prenatal rat heart suggests that these LPA receptors may also contribute to organogenesis. The increase in Lpar3 and Lpar4 expression concomitant with rising expression of cytoskeleton proteins further suggests a possible role for LPA signaling in cytoskeletal remodeling during cardiac development.

The tissue-engineered cardiac patch can alleviate ventricular remodeling and improve functional recovery in experimental myocardial infarction. However, the size of the engineered patch is limited due to insufficient vascularization. This study evaluated the effects of autologous atrial tissue patch cardiomyoplasty and omentopexy in rats with myocardial infarction.Myocardial infarction was induced by left coronary artery ligation in Sprague-Dawley rats. Three weeks later, either a patch of left atrium (A group) or omentum (O group) or both (OA group) were placed over the infarct zone. The atrial tissue patch was harvested from the autologous left atrial appendage along its long axis. The rats in the Control group received rethoracotomy only. After 4 weeks, the survival of the transplanted atrial tissue patch, ventricular remodeling, and cardiac performance were examined.After 4 weeks, surviving myocardium was only detected in the OA group, as indicated by immunolabeling of cardiac troponin-I. Compared with the Control group, only animals in the OA group showed improved heart function assessed by left ventricular ejection fraction (57.9% ± 5.8% vs 47.5% ± 4.5%, p0.05) and left ventricular fractional shortening (25.2% ± 3.6% vs 20.7% ± 2.0%, p0.05). The histologic analysis demonstrated increased scar thickness in the OA group. This was accompanied by increased angiogenesis of the border zone but decreased expression and activity of matrix metalloproteinase and endothelin-1 levels.The omentopexy supported the survival of the autologous atrial tissue patch, which resulted in attenuated ventricular remodeling and restoration of heart function in rats with myocardial infarction. Our findings might represent a novel therapeutic strategy for heart failure.

Low-level laser irradiation (LLLI) has the potential of exerting cardioprotective effect following myocardial infarction (MI). The authors hypothesized that LLLI could influence the expression of cardiac cytokines and contribute to the reversal of ventricular remodeling.LLLI regulates the expression of cytokines after tissue damage. However, little is known concerning the alteration of the cardiac cytokine expression profile after LLLI.MI was created by coronary ligation. The surviving rats were divided randomly into laser and control groups. 33 rats were exposed to a diode laser (635 nm, 5 mW, CW, laser, beam spot size 0.8 cm(2), 6 mW/cm(2), 150 sec, 0.8 J, 1J/cm(2)) as laser group. Another 33 rats received only coronary ligation and served as control group. 28 rats received a thoracotomy without coronary ligation (sham group). One day after laser irradiation, 5 rats from each group were sacrificed and the heart tissues were analyzed by cytokine antibody arrays. Enzyme-linked immunosorbent assay (ELISA) was performed to confirm its reliability. Two weeks after MI, cardiac function and structure were evaluated by echocardiography and histological study.Cytokine antibody array indicated 4 cytokines were significantly changed after laser therapy. ELISA confirmed that granulocyte-macrophage colony stimulating factor and fractalkine were the cytokines involved in the response to therapeutic laser irradiation. However, there was no difference in cytokine release between various groups at 2 weeks after MI. Although LLLI did not improve the damaged heart function, it did reduce the infarct area expansion.The antibody-based protein array technology was applied for screening the cytokine expression profile following MI, with or without laser irradiation. The expression of multiple cytokines was regulated in the acute phase after LLLI. Our results revealed a potential novel mechanism for applying laser therapy to the treatment of heart disease.

Background— Neural remodeling after myocardial infarction (MI) may cause fatal ventricular arrhythmia. Schwann cells (SCs), which are important for neurogenesis, are dramatically reduced after MI. We investigated the feasibility of modifying nervous system regeneration after MI and the efficacy by which it may prevent ventricular arrhythmia following SC transplantation. Methods and Results— Immediately after creation of MI, syngenic Lewis rats were randomized into cell transplantation (n=80) and control groups (n=72). SCs were isolated from sciatic nerves, and 5×10 6 cells were intramyocardially injected into the infarct region. Expression levels of myocardial nerve growth factor, vascular endothelial growth factor, growth-associated protein 43, connexin 43, and laminin in the SC group were significantly higher than control at 7 and 14 days after cell transplantation. Immunohistochemical staining illustrated increases in sympathetic and parasympathetic nerves in both groups. However, SC transplantation significantly increased the parasympathetic/sympathetic ratio at 14 days after cell injection. Dynamic electrocardiography and programmed electric stimulation were also performed. The SCs significantly decreased the low-/high-frequency ratio and arrhythmia score of programmed electric stimulation-induced ventricular arrhythmia at 2 weeks after cell injection. However, SCs did not restore heart function. Conclusion— Transplanted SCs in the infarcted myocardium secrete multiple biological molecules, which alter the ratio of parasympathetic/sympathetic nerve density to normalize irritable myocardium. SC transplantation might be a novel cell-based antiarrhythmic therapy following MI.

Lysophosphatidic acid (LPA), as an endogenous lipid mediator, has been revealed to regulate many important biological and pathophysiological processes via specific G-protein-coupled receptors termed LPA1-5. We have previously shown that LPA antagonized the apoptosis of mesenchymal stem cells (MSCs) induced by hypoxia and serum deprivation (hypoxia/SD), mimicking ischemic myocardium microenvironment. Whether LPA has the same potentially beneficial effect on MSCs in vivo is unknown. Here we demonstrated that LPA treatment improved graft MSC survival in ischemic myocardium assessed in a gender-mismatched transplantation model by real-time PCR, as well as by TUNEL assay. Moreover, transplantation of LPA-treated MSCs enhanced capillary density determined by immunostaining for platelet endothelial cell adhesion molecule (PECAM)-1, and it is also found that LPA enhanced vascular endothelial growth factor (VEGF) release from MSCs under hypoxia/SD in vitro. We did not get any improvement in left ventricular (LV) function at 1 week after transplantation of LPA-treated MSCs. These data suggest that LPA exerts both protective actions on MSC survival and enhancement on MSC paracrine in vivo and may represent a novel and effective treatment strategy in cell transplantation.

Let G be a connected graph of order n and let a,b be two integers such that 2 ≤ a ≤ b. Let g and f be two integer-valued functions defined on V(G) such that a ≤ g(x) ≤ f(x) ≤ b for every x ? V(G). A spanning subgraph F of G is called a (g,f + 1)-factor if g(x) ≤ d F (x) ≤ f(x) + 1 for every x ? V(F). For a subset X of V(G), let $N_{G}(X)=\bigcup \limits _{x\in X}N_{G}(x)$. The binding number of G is defined by $bind(G)=min\{\frac{\mid N_{G}(X) \mid}{\mid X\mid}\mid \emptyset\neq X\subset V(G), N_{G}(X)\neq V(G)\}$. In this paper, it is proved that if $bind(G)> \frac{(a+b)(n-1)}{an}$, f(V(G)) is even and $n\geq \frac{(a+b)^{2}}{a}$, then G has a connected (g,f + 1)-factor.

Let G(V,E) be a simple graph, and let f be an integer function on V with 1 ≤ f(v) ≤ d(v) to each vertex v ? V. An f-edge cover-coloring of a graph G is a coloring of edge set E such that each color appears at each vertex v ? V at least f(v) times. The f-edge cover chromatic index of G, denoted by ?? fc (G), is the maximum number of colors such that an f-edge cover-coloring of G exists. Any simple graph G has f-edge cover chromatic index equal to ? f or ? f -1, where $\delta_{f}=\min\limits^{}_{v\in V}\{\lfloor\frac{d(v)}{f(v)}\rfloor\}$. If ?? fc (G) = ? f , then G is of C f I class; otherwise G is of C f II class. In this paper, we give some sufficient conditions for a graph to be of C f I class, and discuss the classification problem of complete graphs on f-edge cover-coloring.

Objective:To investigate the effect of different soy exposure timings on the mammary tumor development using MMTV-erbB-2 transgenic mice. Furthermore, the underlying mechanisms were also examined. Methods:120 MMTV-erbB-2 transgenic female mice were randomly divided into four groups:control group, early exposure group, late exposure group and lifelong exposure group. The control group mice were treated with soy free diet from week 3 to week 60, the experiment groups mice were treated with soy diet between week 3 to week 12, week 20 to week 60, week 3 to week 60, respectively. Then, the body weight change of each mice, the latency period, and the growth speed of mammary tumor were recorded. Furthermore, the mammary gland morphology was examined by whole mount at 5 weeks. In order to understand the underlying mechanisms of the mammary tumor development, the signal pathways of c-Fos, erbB2 and p-ERK were also examined in breast cancer tissue using immunohistochemistry. Results:We found that the weight in the four groups had no significant difference. Compared with the control group, the TEB numbers and the growth speed of tumors in the early exposure group and the lifelong exposure group were significantly decreased and the tumor latency periods were significantly prolonged (P0.05). Conclusion: Early or lifelong soy exposure affects the morphological development of mammary gland of MMTV-erbB-2 transgenic mice. Soy may display a preventive effect on the initiation of breast cancer. These obersveration may serve as a guide for soy use in the early prevention of the breast cancer. The c-Fos and and p-ERK may be involved in the development of mammary tumor in the MMTV-erbB-2 transgenic mice. The underlying mechanism warrants further studies. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 103rd Annual Meeting of the American Association for Cancer Research; 2012 Mar 31-Apr 4; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2012;72(8 Suppl):Abstract nr 3270. doi:1538-7445.AM2012-3270

A graph G is edge-L-colorable, if for a given edge assignment L={L(e):e@?E(G)}, there exists a proper edge-coloring @f of G such that @f(e)@?L(e) for all e@?E(G). If G is edge-L-colorable for every edge assignment L with |L(e)|>=k for e@?E(G), then G is said to be edge-k-choosable. In this paper, we prove that if G is a planar graph with maximum degree @D(G) 5 and without adjacent 3-cycles, or with maximum degree @D(G) 5,6 and without 7-cycles, then G is edge-(@D(G)+1)-choosable.

The total chromatic number of a graph G, denoted by @g^''(G), is the minimum number of colors needed to color the vertices and edges of G such that no two adjacent or incident elements get the same color. It is known that if a planar graph G has maximum degree @D>=9, then @g^''(G)=@D+1. In this paper, we prove that if G is a planar graph with maximum degree 7, and for every vertex v, there is an integer k"v@?{3,4,5,6} so that v is not incident with any k"v-cycle, then @g^''(G)=8.

Acyclic coloring problem is a specialized problem that arises in the efficient computation of Hessians. A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number @g"a^'(G) of G is the least number of colors in an acyclic edge coloring of G. Alon et al. conjectured that @g"a^'(G)@[email protected](G)+2. In this paper, we consider the sufficient conditions for the planar graphs satisfying @g"a^'(G)@[email protected](G)+1 and @g"a^'(G)[email protected](G).