Chomp on generalized Kneser graphs and others
Combinatorics
2018-04-19 v2
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.
Cite
@article{arxiv.1803.03081,
title = {Chomp on generalized Kneser graphs and others},
author = {Ignacio García-Marco and Kolja Knauer and Luis Pedro Montejano},
journal= {arXiv preprint arXiv:1803.03081},
year = {2018}
}
Comments
17 pages, 4 figures, removed a wrong theorem about almost bipartite graphs from a previous version