5 problems

Let $G$ be a class 2 graph on $n$ vertices, and call a subgraph $H$ overfull when $|E(H)|>\Delta(H)\left\lfloor\frac{|V(H)|}{2}\right\rfloor$. Overfull conjecture. If…

Multigraph Overfull Conjecture. If

Let $G$ be a $Delta$-critical graph of order $n$, meaning that $G$ is critical of class 2 and $Delta(G)=Delta$. Call $G$ just overfull if … The Just Overfull Conjecture. If…

Let $G$ be a simple graph. Write $Delta(G)$ for its maximum degree, let $G_{Delta}$ be the subgraph induced by its maximum-degree vertices, and call $G$ overfull if … A critical cl…

Figueiredo–Meidanis–Mello conjecture. Every Class 2 chordal graph is neighborhood-overfull.