7 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…

Grundy–b-chromatic boundedness conjecture. There exists a function $f$ such that

Boundedness conjecture. The family of b-monotone graphs is $(\Gamma,b)$-bounded.

Havet–Linhares-Sales–Sampaio conjecture. For every $m\geq 3$ and every $G\in\mathcal{B}_m$,

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

Javadi–Omoomi conjecture. For all $n\ge 5$,