F. Dong

activity

20152023

most citedExpression for the Number of Spanning Trees of Line Graphs of Arbitrary Connected Graphs

36 citations · 70 across the 26 of their papers we have counts for

collaborators

27 papers

math.CO2023★ 2 cited

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…

math.CO2023

The absolute values of the perfect matching derangement graph's eigenvalues almost follow the lexicographic order of partitions

Meiqiao Zhang, Fengming Dong

In 2013, Ku and Wong showed that for any partitions $μ$ and $μ^{'}$ of a positive integer $n$ with the same first part $u$ and the lexicographic order $μ ◃ μ^{'}$ , the eigenva…

math.CO2023

Comparing list-color functions of uniform hypergraphs with their chromatic polynomials

Fengming Dong, Meiqiao Zhang

In [J. Combin. Theory Ser. B 161 (2023), 109--119], the authors showed that the list-color function $P_{l} (G, k)$ of any simple graph $G$ of size $m$ coincides with its chromatic poly…

math.CO2023

Compare list-color functions of uniform hypergraphs with their chromatic polynomials (II)

Meiqiao Zhang, Fengming Dong

For any $r$ -uniform hypergraph $H$ with $m$ ( $\geq 2$ ) edges, let $P (H, k)$ and $P_{l} (H, k)$ be the chromatic polynomial and the list-color function of $…

math.CO2022

Comparing list-color functions of uniform hypergraphs with their chromatic polynomials (III)

Fengming Dong, Meiqiao Zhang

For a hypergraph $H$ , let $P (H, k)$ and $P_{l} (H, k)$ be its chromatic polynomial and list-color function respectively, and let $τ^{'} (H)$ be the least non-neg…

math.CO2022

On the size of matchings in 1-planar graph with high minimum degree

Yuanqiu Huang, Zhangdong Ouyang, Fengming Dong

A matching of a graph is a set of edges without common end vertex. A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. Recen…

math.CO2022★ 4 cited

An improved lower bound of $P (G, L) - P (G, k)$ for $k$ -assignments $L$

Fengming Dong, Meiqiao Zhang

Let $G = (V, E)$ be a simple graph with $n$ vertices and $m$ edges, $P (G, k)$ be the chromatic polynomial of $G$ , and $P (G, L)$ be the number of $L$ -colorings of $G$ for any $k$ -assignm…

math.CO2021

Anti-Ramsey numbers for trees in complete multi-partite graphs

Meiqiao Zhang, Fengming Dong

Let $G$ be a complete multi-partite graph of order $n$ . In this paper, we consider the anti-Ramsey number $a r (G, T_{q})$ with respect to $G$ and the set $T_{q}$ …

math.CO2021

$Z_{D P} (n)$ is upperly bounded by $n^{2} - (n + 3) /2$

Meiqiao Zhang, Fengming Dong

DP-coloring was introduced by Dvořák and Postle and is a generalization of proper coloring. For any graph $G$ , let $χ (G)$ and $χ_{D P} (G)$ denote the chromatic number and the DP-chr…

math.CO2021

Express the number of spanning trees in term of degrees

Fengming Dong, Jun Ge, Zhangdong Ouyang

It is well-known that the number of spanning trees, denoted by $τ (G)$ , in a connected multi-graph $G$ can be calculated by the Matrix-Tree theorem and Tutte's deletion-contraction…

math.CO2021

DP color functions versus chromatic polynomials

Fengming Dong, Yan Yang

For any graph $G$ , the chromatic polynomial of $G$ is the function $P (G, m)$ which counts the number of proper $m$ -colorings of $G$ for each positive integer $m$ . The DP color funct…

math.CO2021★ 22 cited

Counting spanning trees in a complete bipartite graph which contain a given spanning forest

Fengming Dong, Jun Ge

In this article, we extend Moon's classic formula for counting spanning trees in complete graphs containing a fixed spanning forest to complete bipartite graphs. Let $(X, Y)$ be the…

math.CO2020

On the sizes of bipartite 1-planar graphs

Yuanqiu Huang, Zhangdong Ouyang, Fengming Dong

A graph is called $1$ -planar if it admits a drawing in the plane such that each edge is crossed at most once. Let $G$ be a bipartite 1-planar graph with $n$ ( $\geq 4$ ) vertices and…

math.CO2020

A Survey of Graph Polynomials Related to the Chromatic Polynomial

Fengming Dong

Introduced by Birkhoff in 1912 to study the four-color conjecture, the chromatic polynomial has become one of the most extensively studied graph polynomials. It is closely connecte…

math.CO2020★ 1 cited

A survey on the study of real zeros of flow polynomials

Fengming Dong

For a bridgeless graph $G$ , its flow polynomial is defined to be the function $F (G, q)$ which counts the number of nonwhere-zero $Γ$ -flows on an orientation of $G$ whenever $q$ is a…

math.CO2020

New upper bounds for the crossing numbers of crossing-critical graphs

Zongpeng Ding, Zhangdong Ouyang, Yuanqiu Huang +1

A graph $G$ is { $k$ -crossing-critical} if $cr (G) \geq k$ , but $cr (G ∖ e) < k$ for each edge $e \in E (G)$ , where $cr (G)$ is the crossing number of $G$ . It is known that for any $k…

math.CO2020

Proving identities on weight polynomials of tiered trees via Tutte polynomials

Fengming Dong, Sherry H. F. Yan

A {\it tiered graph} $G = (V, E)$ with $m$ tiers is a simple graph with $V\subseteq \brk{n}$, where $\brk{n}=\{1,2,\cdots,n\}$, and with a surjective map $t$ from $V$ to $\brk{m}$ su…

math.CO2020★ 3 cited

Upper bounds on the signed edge domination number of a graph

Fengming Dong, Jun Ge, Yan Yang

A signed edge domination function (or SEDF) of a simple graph $G = (V, E)$ is a function $f : E \to {1, - 1}$ such that $\sum_{e^{'} \in N [e]} f (e^{'}) \geq 1$ holds for each edge $e\in E…

math.CO2019

New expressions for order polynomials and chromatic polynomials

Fengming Dong

Let $G = (V, E)$ be a simple graph with $V = {1, 2, \dots, n}$ and $χ (G, x)$ be its chromatic polynomial. For an ordering $π = (v_{1}, v_{2}, \dots, v_{n})$ of elements of $V$ , let $δ_{G} (π)$ be the…

math.CO2019

The rank of a complex unit gain graph in terms of the matching number

Shengjie He, Rong-Xia Hao, Fengming Dong

A complex unit gain graph (or $T$ -gain graph) is a triple $Φ = (G, T, φ)$ (or $(G, φ)$ for short) consisting of a simple graph $G$ , as the underlying graph of $(G…

math.CO2019

Formulas counting spanning trees in line graphs and their extensions

Fengming Dong

For any connected multigraph $G = (V, E)$ and any $M \subseteq E$ , if $M$ induces an acyclic subgraph of $G$ and removing all edges in $M$ yields a subgraph of $G$ whose components are…

math.CO2019

Spanning trees in complete bipartite graphs and resistance distance in nearly complete bipartite graphs

Jun Ge, Fengming Dong

Using the theory of electrical network, we first obtain a simple formula for the number of spanning trees of a complete bipartite graph containing a certain matching or a certain t…

math.CO2018★ 1 cited

On non-feasible edge sets in matching-covered graphs

Xiao Zhao, Fengming Dong, Sheng Chen

Let $G = (V, E)$ be a matching-covered graph and $X$ be an edge set of $G$ . $X$ is said to be feasible if there exist two perfect matchings $M_{1}$ and $M_{2}$ in $G$ such that $|M_1\cap…

math.CO2018

Zero-free intervals of chromatic polynomials of mixed hypergraphs

Ruixue Zhang, Fengming Dong

In this paper, we prove that $(- \infty, 0)$ is a zero-free interval for chromatic polynomials of a family $L_{0}$ of hypergraphs and $(0, 1)$ is a zero-free interval for chrom…

On the maximum local mean order of sub-k-trees of a k-tree

The absolute values of the perfect matching derangement graph's eigenvalues almost follow the lexicographic order of partitions

Comparing list-color functions of uniform hypergraphs with their chromatic polynomials

Compare list-color functions of uniform hypergraphs with their chromatic polynomials (II)

Comparing list-color functions of uniform hypergraphs with their chromatic polynomials (III)

On the size of matchings in 1-planar graph with high minimum degree

An improved lower bound of P(G,L)−P(G,k) for k-assignments L

Anti-Ramsey numbers for trees in complete multi-partite graphs

ZDP​(n) is upperly bounded by n2−(n+3)/2

Express the number of spanning trees in term of degrees

DP color functions versus chromatic polynomials

Counting spanning trees in a complete bipartite graph which contain a given spanning forest

On the sizes of bipartite 1-planar graphs

A Survey of Graph Polynomials Related to the Chromatic Polynomial

A survey on the study of real zeros of flow polynomials

New upper bounds for the crossing numbers of crossing-critical graphs

Proving identities on weight polynomials of tiered trees via Tutte polynomials

Upper bounds on the signed edge domination number of a graph

New expressions for order polynomials and chromatic polynomials

The rank of a complex unit gain graph in terms of the matching number

Formulas counting spanning trees in line graphs and their extensions

Spanning trees in complete bipartite graphs and resistance distance in nearly complete bipartite graphs

On non-feasible edge sets in matching-covered graphs

Zero-free intervals of chromatic polynomials of mixed hypergraphs

An improved lower bound of $P (G, L) - P (G, k)$ for $k$ -assignments $L$

$Z_{D P} (n)$ is upperly bounded by $n^{2} - (n + 3) /2$