2 citations · 2 across the 8 of their papers we have counts for
9 papers
On minimum-size matroid counterexamples to the multiplicative Merino--Welsh inequality
Jungang Chen, Xian'an Jin, Tianlong Ma
Let be a matroid and let $\Tutte_M(x,y)$ be its Tutte polynomial. The multiplicative Merino--Welsh inequality \[ \Tutte_M(2,0)\Tutte_M(0,2)\geq \Tutte_M(1,1)^2 \] was proved to…
Proof of a Brown-Mol conjecture on subtree roots
Xian'an Jin, Tianlong Ma, Yi Wang
The subtree polynomial of a tree is the generating function that enumerates its subtrees according to their orders. Brown and Mol conjectured that every subtree root of a tree of o…
Irreducibility of interlace polynomials
Jungang Chen, Xian'an Jin, Tianlong Ma
The factorisation of graph polynomials often reflects combinatorial decomposition. For a nonempty loopless graph , we first prove that the two-variable interlace polynomial $q(G…
Combinatorial interpretations of Tutte polynomials at the point
Yu Chen, Xian'an Jin, Tianlong Ma
Let be a simple connected graph, and let be the Tutte polynomial of . Motivated by the works in \cite{Ma}, we, in this paper, introduce the even-left spanning f…
On the coefficients of interior and exterior polynomials of polymatroids
Xiaxia Guan, Xian'an Jin, Tianlong Ma +1
The Tutte polynomial is an important invariant of graphs and matroids. Chen and Guo \emph{[Adv. in Appl. Math. 166 (2025) 102868.]} proved that for a -edge connected graph $…
Coefficients of univariate Tutte polynomials with one variable fixed
Tianlong Ma, Xiaxia Guan, Xian'an Jin +1
It is well known that the 2-variable Tutte polynomial of a graph includes chromatic polynomial and flow polynomial of , i.e. the cases of and . In 2013, Kálmán in…
Convolution formulas for multivariate arithmetic Tutte polynomials
Tianlong Ma, Xian'an Jin, Weiling Yang
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 form…
On the maximum local mean order of sub-k-trees of a k-tree
Zhuo Li, Tianlong Ma, Fengming Dong +1
For a k-tree T, a generalization of a tree, the local mean order of sub-k-trees of T is the average order of sub-k-trees of T containing a given k-clique. The problem whether the l…
Extreme coefficients of multiplicity Tutte polynomials
Xian'an Jin, Tianlong Ma, Weiling Yang
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 ex…