Hat guessing number of planar graphs is at least 22

Aleksei Latyshev; Konstantin Kokhas

Hat guessing number of planar graphs is at least 22

Combinatorics 2023-01-26 v1

Authors: Aleksei Latyshev , Konstantin Kokhas

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 ${\text{HG}}_1(G) \ge 22$ .

Keywords

hat guessing number deterministic hats game planar graph winning strategy graph constructors paths petunias

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@article{arxiv.2301.10305,
  title  = {Hat guessing number of planar graphs is at least 22},
  author = {Aleksei Latyshev and Konstantin Kokhas},
  journal= {arXiv preprint arXiv:2301.10305},
  year   = {2023}
}

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23 pages

Hat guessing number of planar graphs is at least 22

Abstract

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