6 problems

Let $G$ be a finite simple graph. For a non-empty subgraph $H$ of $G$, define its Ore-degree in $G$ by … with $\sigma_G(H)=0$ when $H$ is empty. Suppose that $H$ is a bipartite sub…

Ore-degree Erdős Matching Conjecture. If $n>rs$ and

For a graph $G$, define its Ore-degree by … A graph is SE $k$-choosable if every $k$-list assignment admits a strongly equitable list coloring. Strongly equitable Ore-degree conjec…

For a graph $G$, define its Ore-degree by … A graph is equitably $k$-choosable if every $k$-list assignment admits a proper coloring in which each color class has size at most…

Let $k\geq3$, and let a $k$-decomposable graph be one admitting the $k$-decomposition defined in the source. Strong Ore-degree Chen–Lih–Wu conjecture. If $G$ is a $k$-colorable gra…

For a graph $G$, define its Ore-degree by … A proper coloring is equitable when its color classes differ in size by at most one. Kostochka–Kierstead's Ore-degree conjecture. Let…