6 papers
A recursive definition for the polymatroid Tutte polynomial
Xiaxia Guan, Xian'an Jin, Weiling Yang
The Tutte polynomial is a significant invariant of graphs and matroids. It is well-known that it has three equivalent definitions: bases expansion, rank generating function, and de…
A sharp upper bound for the number of connected sets in any grid graph
Hongxia Ma, Xian'an Jin, Weiling Yang +1
A connected set in a graph is a subset of vertices whose induced subgraph is connected. Although counting the number of connected sets in a graph is generally a \#P-complete proble…
Isolation partitions in graphs
Gang Zhang, Weiling Yang, Xian'an Jin
Let be a graph and an integer. A subset is a -clique (resp., cycle) isolating set of if contains no -clique (resp., cycle). 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…
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…
On the polymatroid Tutte polynomial
Xiaxia Guan, Weiling Yang, Xian'an Jin
The Tutte polynomial is a well-studied invariant of matroids. The polymatroid Tutte polynomial , introduced by Bernardi et al., is an extension of the classic…