Overfull Conjecture for graphs with maximum degree 4

Chunhui Ge; Gregory Gutin; Xuli Qi

Overfull Conjecture for graphs with maximum degree 4

Combinatorics 2026-07-12 v1

Authors: Chunhui Ge , Gregory Gutin , Xuli Qi

Abstract

Let $G$ be a simple graph with maximum degree $\Delta(G)$ . The graph $G$ is overfull if $\left|E(G)\right|> \Delta(G)\lfloor |V(G)|/2\rfloor$ . In 1986, Chetwynd and Hilton proposed the Overfull Conjecture: If $G$ is a simple graph with $\Delta(G)>\frac{|V(G)|}{3}$ , then $G$ is a Class $2$ graph if and only if $G$ contains an overfull subgraph $H$ with $\Delta(H)=\Delta(G)$ . In this paper, we give a proof of this conjecture for graphs with maximum degree $4$ .

Cite

@article{arxiv.2607.10947,
  title  = {Overfull Conjecture for graphs with maximum degree 4},
  author = {Chunhui Ge and Gregory Gutin and Xuli Qi},
  journal= {arXiv preprint arXiv:2607.10947},
  year   = {2026}
}