5 problems

LMW conjecture. With high probability,

Let $G_{n,p}$ be the random graph on $n$ vertices in which each edge is present independently with probability $p=p(n)$, and let $\chi_c(G_{n,p})$ denote its clique chromatic numbe…

A clique coloring of a graph is a vertex coloring in which no maximal clique is monochromatic; a graph is $k$-clique colorable if it has a clique coloring with $k$ colors. A graph…

A $B_1$-EPG graph is the edge-intersection graph of paths in a rectangular grid, with each path having at most one bend. A graph is 3-clique colorable if its vertices can be colore…

A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of its largest clique. A graph is 3-clique colorable if its vertices can be color…