4 problems

Let $G$ be an $\overline{\chi}_{\geqslant}$-edge-critical graph with at least two edges, and let $e,f\in E(G)$. The mixed edge-deletion conjecture. It is impossible that … The clai…

Let $G$ be a graph. Write $\overline{\chi}_{\geqslant}(G)$ for its majority $C$-chromatic number, and call $G$ $\overline{\chi}_{\geqslant}$-edge-critical if it has at least one ed…

Let $D$ be a countable acyclic digraph. A vertex coloring of $D$ is a majority coloring if, at every vertex, at most half of its outgoing edges are bad, meaning that their endpoint…

Let $G$ be a countable graph, and assign to each vertex $v$ a list $L(v)$ of available colors. The graph is majority $k$-choosable if, for every such assignment with $|L(v)|=k$, it…