Hat Guessing on Books and Windmills
Combinatorics
2020-10-27 v1
Abstract
The hat-guessing number is a graph invariant defined by Butler, Hajiaghayi, Kleinberg, and Leighton. We determine the hat-guessing number exactly for book graphs with sufficiently many pages, improving previously known lower bounds of He and Li and exactly matching an upper bound of Gadouleau. We prove that the hat-guessing number of is , making this the first complete bipartite graph for which the hat-guessing number is known to be smaller than the upper bound of of Gadouleau and Georgiou. Finally, we determine the hat-guessing number of windmill graphs for most choices of parameters.
Cite
@article{arxiv.2010.13249,
title = {Hat Guessing on Books and Windmills},
author = {Xiaoyu He and Yuzu Ido and Benjamin Przybocki},
journal= {arXiv preprint arXiv:2010.13249},
year = {2020}
}