Guangming Jing

activity

20182022

collaborators

6 papers

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

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

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.CO2018

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…