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Hat guessing number of planar graphs is at least 22 (2301.10305v1)
Published 24 Jan 2023 in math.CO
Abstract: We analyze the version of the deterministic Hats game. In this paper, we present new constructors, i.e. theorems that allow built winning strategies for the sages on different graphs. Using this technique we calculate the hat guessing number ${\text{HG}}_s(G)$ for paths and "petunias", and present a planar graph $G$ for which ${\text{HG}}_1(G) \ge 22$.