Guangming Jing

activity

20132023

most citedProof of the Goldberg-Seymour Conjecture on Edge-Colorings of Multigraphs

12 citations · 17 across the 14 of their papers we have counts for

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14 papers · 1 filter

math.CO2023

On Edge Coloring of Multigraphs

Guangming Jing

Let $Δ (G)$ and $χ^{'} (G)$ be the maximum degree and chromatic index of a graph $G$ , respectively. Gupta\,(1967), Goldberg\,(1973), Andersen\,(1977), and Seymour\,(1979) made the follo…

math.CO2022

Decomposition of class II graphs into two class I graphs

Yan Cao, Guangming Jing, Rong Luo +3

Mkrtchyan and Steffen [J. Graph Theory, 70 (4), 473--482, 2012] showed that every class II simple graph can be decomposed into a maximum $Δ$ -edge-colorable subgraph and a matching.…

math.CO2022

Overfullness of edge-critical graphs with small minimal core degree

Yan Cao, Guantao Chen, Guangming Jing +1

Let $G$ be a simple graph. Denote by $n$ , $Δ (G)$ and $χ^{'} (G)$ be the order, the maximum degree and the chromatic index of $G$ , respectively. We call $G$ \emph{overfull} if $|E(G)|/…

math.CO2022

Precoloring extension of Vizing's Theorem for multigraphs

Yan Cao, Guantao Chen, Guangming Jing +2

Let $G$ be a graph with maximum degree $Δ (G)$ and maximum multiplicity $μ (G)$ . Vizing and Gupta, independently, proved in the 1960s that the chromatic index of $G$ is at most $Δ(G)…

math.CO2021

A note on Goldberg's conjecture on total chromatic numbers

Yan Cao, Guantao Chen, Guangming Jing

Let $G = (V (G), E (G))$ be a multigraph with maximum degree $Δ (G)$ , chromatic index $χ^{'} (G)$ and total chromatic number $χ^{''} (G)$ . The Total Coloring conjecture proposed by Behzad and V…

math.CO2021

The Core Conjecture of Hilton and Zhao II: a Proof

Yan Cao, Guantao Chen, Guangming Jing +1

A simple graph $G$ with maximum degree $Δ$ is overfull if $∣ E (G) ∣ > Δ ⌊ ∣ V (G) ∣/2 ⌋$ . The core of $G$ , denoted $G_{Δ}$ , is the subgraph of $G$ induced by its vertices of degre…

math.CO2021★ 1 cited

Pseudo-multifan and Lollipop

Yan Cao, Guantao Chen, Guangming Jing +1

A simple graph $G$ with maximum degree $Δ$ is \emph{overfull} if $∣ E (G) ∣ > Δ ⌊ ∣ V (G) ∣/2 ⌋$ . The \emph{core} of $G$ , denoted $G_{Δ}$ , is the subgraph of $G$ induced by its ver…

math.CO2021

The overfullness of graphs with small minimum degree and large maximum degree

Yan Cao, Guantao Chen, Guangming Jing +1

Given a simple graph $G$ , denote by $Δ (G)$ , $δ (G)$ , and $χ^{'} (G)$ the maximum degree, the minimum degree, and the chromatic index of $G$ , respectively. We say $G$ is \emph{ $Δ$ -critic…

math.CO2020★ 3 cited

Proof of the Core Conjecture of Hilton and Zhao

Yan Cao, Guantao Chen, Guangming Jing +1

Let $G$ be a simple graph with maximum degree $Δ$ . We call $G$ \emph{overfull} if $∣ E (G) ∣ > Δ ⌊ ∣ V (G) ∣/2 ⌋$ . The \emph{core} of $G$ , denoted $G_{Δ}$ , is the subgraph of $G$ i…

math.CO2019

On Gupta's Co-density Conjecture

Yan Cao, Guantao Chen, Guoli Ding +2

Let $G = (V, E)$ be a multigraph. The {\em cover index} $ξ (G)$ of $G$ is the greatest integer $k$ for which there is a coloring of $E$ with $k$ colors such that each vertex of $G$ is…

math.CO2019★ 12 cited

Proof of the Goldberg-Seymour Conjecture on Edge-Colorings of Multigraphs

Guantao Chen, Guangming Jing, Wenan Zang

Given a multigraph $G = (V, E)$ , the {\em edge-coloring problem} (ECP) is to color the edges of $G$ with the minimum number of colors so that no two adjacent edges have the same color…

math.CO2018★ 1 cited

Independence number of edge-chromatic critical graphs

Yan Cao, Guantao Chen, Guangming Jing +1

Let $G$ be a simple graph with maximum degree $Δ (G)$ and chromatic index $χ^{'} (G)$ . A classic result of Vizing indicates that either $χ^{'} (G) = Δ (G)$ or $χ^{'} (G) = Δ (G) + 1$ . The graph $G$ i…

math.CO2017

Structural properties of edge-chromatic critical multigraphs

Guantao Chen, Guangming Jing

Appearing in different format, Gupta\,(1967), Goldberg\,(1973), Andersen\,(1977), and Seymour\,(1979) conjectured that if $G$ is an edge- $k$ -critical graph with $k \geq Δ + 1$ , then $…

math.CO2013

Sign patterns with minimum rank 3 and point-line configurations

Guangming Jing, Wei Gao, Yubin Gao +4

A \emph{sign pattern (matrix)} is a matrix whose entries are from the set ${+, -, 0}$ . The \emph{minimum rank} (respectively, \emph{rational minimum rank}) of a sign pattern matr…