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290 results on '"Yang, Weiling"'

1. Isolation partitions in graphs

Author

Zhang, Gang, Yang, Weiling, and Jin, Xian'an

Subjects
Mathematics - Combinatorics, 05C69, 05C15
Abstract

Let $G$ be a graph and $k \geq 3$ an integer. A subset $D \subseteq V(G)$ is a $k$-clique (resp., cycle) isolating set of $G$ if $G-N[D]$ contains no $k$-clique (resp., cycle). In this paper, we prove that every connected graph with maximum degree at most $k$, except $k$-clique, can be partitioned into $k+1$ disjoint $k$-clique isolating sets, and that every connected claw-free subcubic graph, except 3-cycle, can be partitioned into four disjoint cycle isolating sets. As a consequence of the first result, every $k$-regular graph can be partitioned into $k+1$ disjoint $k$-clique isolating sets., Comment: 14 pages, 5 figures

Published
2024

2. Convolution formulas for multivariate arithmetic Tutte polynomials

Author

Ma, Tianlong, Jin, Xian'an, and Yang, Weiling

Subjects
Mathematics - Combinatorics
Abstract

The multivariate arithmetic Tutte polynomial of arithmetic matroids is a generalization of the multivariate Tutte polynomial of matroids. In this note, we give the convolution formulas for the multivariate arithmetic Tutte polynomial of the product of two arithmetic matroids. In particular, the convolution formulas for the multivariate arithmetic Tutte polynomial of an arithmetic matroid are obtained. Applying our results, several known convolution formulas including [5, Theorem 10.9 and Corollary 10.10] and [1, Theorems 1 and 4] are proved by a purely combinatorial proof. The proofs presented here are significantly shorter than the previous ones. In addition, we obtain a convolution formula for the characteristic polynomial of an arithmetic matroid.

Published
2023

3. Extreme coefficients of multiplicity Tutte polynomials

Author

Jin, Xian'an, Ma, Tianlong, and Yang, Weiling

Subjects
Mathematics - Combinatorics
Abstract

The multiplicity Tutte polynomial, which includes the arithmetic Tutte polynomial, is a generalization of the classical Tutte polynomial of matroids. In this paper, we obtain an expression of the general coefficient and the expressions of six extreme coefficients of multiplicity Tutte polynomials. In particular, an expression of the general coefficient and the expressions of corresponding extreme coefficients of classical Tutte polynomial of matroids are deduced.

Published
2023

4. On the polymatroid Tutte polynomial

Author

Guan, Xiaxia, Yang, Weiling, and Jin, Xian'an

Subjects
Mathematics - Combinatorics
Abstract

The Tutte polynomial is a well-studied invariant of matroids. The polymatroid Tutte polynomial $\mathcal{J}_{P}(x,y)$, introduced by Bernardi et al., is an extension of the classical Tutte polynomial from matroids to polymatroids $P$. In this paper, we first prove that $\mathcal{J}_{P}(x,t)$ and $\mathcal{J}_{P}(t,y)$ are interpolating for any fixed real number $t\geq 1$, and then we study the coefficients of high-order terms in $\mathcal{J}_{P}(x,1)$ and $\mathcal{J}_{P}(1,y)$. These results generalize results on interior and exterior polynomials of hypergraphs., Comment: 14 pages, 0 figures

Published
2022

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