3 problems

Let $G$ and $H$ be graphs, let $k\text{?}$ be a positive integer, and write $\varphi$ for the $b$-chromatic number and $G^k$ for the $k$-th graph power. Cartesian-product power con…

Let $G$ be the tensor product of two distinct star graphs $S_n$ and $S_m$. Star-graph tensor-product conjecture. The $b$-chromatic number of $G$ is $m+n+1$. This conjecture propose…

Blidia–Maffray–Zemir conjecture. If $G$ is not the Petersen graph, then