Back to Search
Start Over
PERFECT MATCHING INDEX VERSUS CIRCULAR FLOW NUMBER OF A CUBIC GRAPH.
- Source :
- SIAM Journal on Discrete Mathematics; 2021, Vol. 35 Issue 2, p1287-1297, 11p
- Publication Year :
- 2021
-
Abstract
- The perfect matching index of a cubic graph G, denoted by \pi (G), is the smallest number of perfect matchings that cover all the edges of G. According to the Berge--Fulkerson conjecture, \pi (G) \leq 5 for every bridgeless cubic graph G. The class of graphs with \pi \geq 5 is of particular interest as many conjectures and open problems, including the famous cycle double cover conjecture, can be reduced to it. Although nontrivial examples of such graphs are very difficult to find, a few infinite families are known, all with circular flow number \Phi c(G) = 5. It has been therefore suggested [Abreu et al., Electron. J. Combin., 23 (2016), P3.54] that \pi (G) \geq 5 might imply \Phi c(G) \geq 5. In this article we dispel these hopes and present a family of cyclically 4-edgeconnected cubic graphs of girth at least 5 with \pi \geq 5 and \Phi c \leq 4 + 2 3. [ABSTRACT FROM AUTHOR]
- Subjects :
- LOGICAL prediction
ELECTRONS
SPEED of light
EDGES (Geometry)
Subjects
Details
- Language :
- English
- ISSN :
- 08954801
- Volume :
- 35
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 154646091
- Full Text :
- https://doi.org/10.1137/20M1359407