Hat guessing number of planar graphs is at least 22

TL;DR

This paper investigates the hat guessing game on graphs, introducing new theorems to construct winning strategies, and establishes that certain planar graphs have a hat guessing number of at least 22.

Contribution

The paper develops new theorems for constructing winning strategies and determines the hat guessing number for specific graphs, including a planar graph with a guessing number of at least 22.

Findings

Calculated hat guessing number for paths and petunias.

Presented a planar graph with HG_1(G) ≥ 22.

Developed new theorems for strategy construction.

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