3 problems

Let $B_{2,n}$ denote the two-spine book graph with $n$ pages, and let $\operatorname{HGP}(G)$ be the proper hat-guessing number of a graph $G$. Two-spine book graph conjecture. For…

Let $\widehat{\mathcal{S}}_1$ be the class of standard-imaginary strategies and let $\widehat{\mathcal{M}}_1$ be the class of imaginary strategies used in the continuous Levine gam…

Let $G$ be a cycle $C_n$ and let $h$ be a hat function such that $2 \leq h(v) \leq 4$ for every vertex $v$. Let $A\in V(G)$ be such that $h(A)=2$. The game…