4 problems

For a sequence $S=(s_1,dots,s_k)$ of non-decreasing positive integers, an $S$-packing edge-coloring of a graph $G$ is a partition of $E(G)$ into $E_1,dots,E_k$ such that the distan…

Hocquard–Lajou–Lužar conjecture. Every subcubic planar graph has an $(1^2,2^3)$-packing edge-coloring.

A subcubic graph is a graph $G$ with maximum degree $Delta(G)\leq 3$. An $(1^2,2^4)$-coloring is a partition of $E(G)$ into two matchings and four induced matchings. Hocquard–Lajou…

Subdivision packing-coloring conjecture. The graph $S(G)$ admits a $(1,2,3,4,5)$-packing coloring. Equivalently, every subdivision of a subcubic graph has packing chromatic number…