# On the hat guessing number of a planar graph class

@article{Bradshaw2021OnTH,
title={On the hat guessing number of a planar graph class},
journal={J. Comb. Theory, Ser. B},
year={2021},
volume={156},
pages={174-193}
}
2 Citations

## Figures from this paper

### On the hat guessing number and guaranteed subgraphs

The hat guessing number of a graph is a parameter related to the hat guessing game for graphs introduced by Winkler. In this paper, we show that graphs of sufficiently large hat guessing number must

### Hat guessing numbers of strongly degenerate graphs

• Mathematics
• 2021
Assume n players are placed on the n vertices of a graph G. The following game was introduced by Winkler: An adversary puts a hat on each player, where each hat has a colour out of q available

## References

SHOWING 1-10 OF 20 REFERENCES

### Hat Guessing on Books and Windmills

• Mathematics
Electron. J. Comb.
• 2022
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,

### The Hats Game. the Power of Constructors

• Mathematics
• 2021
We analyze the following general version of the deterministic Hats game. Several sages wearing colored hats occupy the vertices of a graph. Each sage can have a hat of one of k colors. Each sage

### The Hat Guessing Number of Graphs

• Mathematics
2019 IEEE International Symposium on Information Theory (ISIT)
• 2019
It is shown that under certain conditions, the linear hat guessing number of Kn,n is at most 3, exhibiting a huge gap from the $\Omega \left( {{n^{\frac{1}{2} - o(1)}}} \right)$ (nonlinear) hat guessingNumber of this graph.

### The Three Colour Hat Guessing Game on Cycle Graphs

It is proved that a winning strategy exists if and only if $N$ is divisible by $3$ or $N=4$ and a predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colours.

### New Constructions and Bounds for Winkler's Hat Game

• Mathematics, Computer Science
SIAM J. Discret. Math.
• 2015
This paper discovers some new classes of graphs which allow a winning strategy in the hat game, thus answering some of the open questions in Butler et al.

### Cliques and Constructors in “Hats” Game. I

• Mathematics
• 2020
We analyze the following general variant of deterministic "Hats" game. Several sages wearing colored hats occupy the vertices of a graph, $k$-th sage can have hats of one of $h(k)$ colors. Each sage

### Hat Guessing Games

• Computer Science
SIAM Rev.
• 2008
This paper considers several variants of the hat guessing problem, united by the common theme that the guessing strategies are required to be deterministic and the objective is to maximize the number of correct answers in the worst case.

### The Cops and Robber game on graphs with forbidden (induced) subgraphs

• Mathematics
Contributions Discret. Math.
• 2010
This paper completely characterize (for both relations) the graphs which force bounded cop number in the classes of graphs defined by forbidding one or more graphs as either sub graphs or induced subgraphs and bound theCop number in terms of the tree-width.

### Bounding the Cop Number of a Graph by Its Genus

• Mathematics
SIAM J. Discret. Math.
• 2021
The first improvement to Schroder's bound on cop number of a connected graph is given, showing that c(G) is bounded as a function of the genus of the graph g(G).

### Hat Guessing Numbers of Degenerate Graphs

• Mathematics
Electron. J. Comb.
• 2020
It is shown that for all $d\ge 1$ there exists a $d-degenerate graph$G$for which$\text{HG}(G) \ge 2^{2^{d-1}}\$ is possible.