Yonglei Chen | Searcharxiv

arXiv2025

Short Brooms in Edge-chromatic Critical Graphs

This paper studies short brooms in edge-chromatic critical graphs. We prove that for any short broom in a $Δ$-critical graph, at most one color is missing at more than one vertex. Moreover, this color (if exists) is missing at exactly two vertices. Applying this result, we verify the Vertex-splitting Conjecture for graphs with $Δ\geq 2(n-1)/3$ and the Overfull Conjecture for $Δ$-critical graphs satisfying $Δ\geq (2n+5δ-12)/3$.

math.CO↗

arXiv2022

Spectral radius conditions for fractional $[a,b]$-covered graphs

A graph $G$ is called fractional $[a,b]$-covered if for every edge $e$ of $G$ there is a fractional $[a,b]$-factor with the indicator function $h$ such that $h(e)=1$. In this paper, we provide tight spectral radius conditions for graphs being fractional $[a,b]$-covered.

math.CO↗