Chomp on generalized Kneser graphs and others

TL;DR

This paper analyzes the game of chomp played on generalized Kneser graphs, Johnson graphs, and threshold graphs, determining winning strategies and Nim-values for these classes.

Contribution

It provides explicit strategies and Nim-value computations for chomp on these graph classes, extending previous results to broader families.

Findings

Determined winning strategies for chomp on generalized Kneser and Johnson graphs.

Calculated Nim-values for these graph classes.

Extended results to clique complexes and threshold graphs.

Abstract

In chomp on graphs, two players alternatingly pick an edge or a vertex from a graph. The player that cannot move any more loses. The questions one wants to answer for a given graph are: Which player has a winning strategy? Can a explicit strategy be devised? We answer these questions (and determine the Nim-value) for the class of generalized Kneser graphs and for several families of Johnson graphs. We also generalize some of these results to the clique complexes of these graphs. Furthermore, we determine which player has a winning strategy for some classes of threshold graphs.