12 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…
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…
A direct proof of well-definedness for the polymatroid Tutte polynomial
Xiaxia Guan, Xian'an Jin
For a polymatroid over , Bernardi, Kálmán and Postnikov [\emph{Adv. Math.} 402 (2022) 108355] introduced the polymatroid Tutte polynomial relying on the…
A deletion-contraction formula and monotonicity properties for the polymatroid Tutte polynomial
Xiaxia Guan, Xian'an Jin, Tamás Kálmán
The Tutte polynomial is a fundamental invariant of matroids. The polymatroid Tutte polynomial , introduced by Bernardi, Kálmán, and Postnikov, is an extension…
Extremal trees with respect to spectral radius of restrictedly weighted adjacency matrices
Ruiling Zheng, Xiaxia Guan, Xian an Jin
For a graph and , denote by the degree of vertex . Let be a real symmetric function in and . The weighted adjacency matrix $…
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…
Tight toughness, isolated toughness and binding number bounds for the -factors
Xiaxia Guan, Tianlong Ma, Chao Shi
The -factor of a graph is a spanning subgraph whose each component is either or . In this paper, a sufficient condition with regard to tight toughness, isol…
On coefficients of the interior and exterior polynomials
Xiaxia Guan, Xian'an Jin
The interior polynomial and the exterior polynomial are generalizations of valuations on and of the Tutte polynomial of graphs to hypergraphs, respec…
A direct and elementary proof of the well-definedness of the interior and exterior polynomials of hypergraphs
Xiaxia Guan, Xian'an Jin, Tianlong Ma
T. Kálmán (A version of Tutte's polynomial for hypergraphs, Adv. Math. 244 (2013) 823-873.) introduced the interior and exterior polynomials which are generalizations of the Tutte…
Minimum degree and size conditions for the proper connection number of graphs
Xiaxia Guan, Lina Xue, Eddie Cheng +1
An edge-coloured graph is called if every two vertices are connected by a proper path. The of a connected graph , denot…
Embedding 5-planar graphs in three pages
Xiaxia Guan, Weihua Yang
A \emph{book-embedding} of a graph is an embedding of vertices of along the spine of a book, and edges of on the pages so that no two edges on the same page intersect.…