4 problems

Let $k$ be a positive integer. A graph $H$ is $k$-divisible if … for every vertex $u\in V(H)$. Alon–Friedland–Kalai conjecture. If $G$ is a graph on $n$ vertices that does not cont…

Let $k$ be a positive integer. A $0_{q(k)}$-graph is the graph class defined in the source, and $\chi'_k(G)$ is the mod $k$ chromatic index. $0_{q(k)}$-graph conjecture. For every…

Let $k$ be a positive integer. A $0_k$-graph is the graph class defined in the source, and $\chi'_k(G)$ is the mod $k$ chromatic index. $0_k$-graph conjecture. For every $0_k$-grap…

Let $G$ be a simple graph and let $k\geq 2$ be an integer. A $\chi'_{k}$-coloring of $G$ is an edge coloring such that the subgraph induced by the edges of each color has all degre…