4 problems

For a graph $F$, an $F$-free graph has no induced subgraph isomorphic to $F$; a graph is $(T,C_4)$-free if it is both $T$-free and $C_4$-free. Here $\chi_s$ denotes the star chroma…

For a graph $G$, the star chromatic number $\chi_s(G)$ is the minimum number of colors in a proper coloring such that any two color classes induce a star forest. A graph is…

Let $C_m$ and $C_n$ be cycles of lengths $m,n\geq 3$, and let $\square$ denote the Cartesian graph product. The star chromatic number $\chi_s(G)$ is the least number of colors in a…

Six-color conjecture. If $G$ is a subcubic graph, then