7 problems

Casselgren, Markström and Pham's conjecture. If $n$ and $d$ are positive integers, and $\varphi$ is a proper edge-precoloring of $K_{n,n}^d$ with at most $nd-1$ precolored edges, t…

Balanced complete-bipartite Cartesian-product conjecture. If any precoloring of at most $k < r$ edges of $G$ can be extended to a proper $\chi'(G)$-edge-coloring of $G$, then any p…

General Cartesian-product conjecture. Every precoloring of at most $k+l+1$ edges of $G \square H$ is extendable to a proper $(\chi'(G)+\chi'(H))$-edge-coloring of $G \square H$.

Casselgren, Petros and Fufa's conjecture. If every precoloring of at most $k < \chi'(G)$ edges of $G$ can be extended to a proper $\chi'(G)$-edge-coloring, then every precoloring o…

Cartesian-product precoloring extension conjecture. This precoloring is extendable to a proper edge coloring.

Generic precoloring-extension conjecture. For every positive even integer $\ell$, there exists an integer $d$ such that, if no 4-cycle in $G-U$ separates a face of $S$ from the out…

Let $G$ be a graph, let $k$ be an integer, and write $G\square K_2$ for the cartesian product of $G$ and the complete graph on two vertices. Write $\chi'(G)$ for the edge-chromatic…