4 problems

Let $G$ be a graph, let $\Delta(G)$ denote its maximum degree, and let $a'(G)$ denote the least number of colours in an acyclic edge colouring of $G$. Fiamčík–Alon–Sudakov–Zaks con…

Let $G$ be a simple finite graph, let $\Delta=\Delta(G)$ be its maximum degree, and let $a'(G)$ denote the minimum number of colours in a proper edge colouring of $G$ such that the…

Let $G$ be a subcubic graph, meaning that every vertex of $G$ has degree at most $3$. Let $\chi_{\nu}(G)$ denote the new vertex chromatic number introduced in the paper. Subcubic v…

Let $G$ be a graph, and let $a'(G)$ denote its acyclic chromatic index and $\Delta(G)$ its maximum degree. Alon's conjecture. … This is the foundational conjecture in acyclic edge…