A vertex and edge deletion game on graphs
Combinatorics
2018-10-23 v2 Discrete Mathematics
Abstract
Starting with a graph, two players take turns in either deleting an edge or deleting a vertex and all incident edges. The player removing the last vertex wins. We review the known results for this game and extend the computation of nim-values to new families of graphs. A conjecture of Khandhawit and Ye on the nim-values of graphs with one odd cycle is proved. We also see that, for wheels and their subgraphs, this game exhibits a surprising amount of unexplained regularity.
Keywords
Cite
@article{arxiv.1709.01354,
title = {A vertex and edge deletion game on graphs},
author = {Cormac O'Sullivan},
journal= {arXiv preprint arXiv:1709.01354},
year = {2018}
}
Comments
25 pages, 29 figures, minor corrections and improvements, appearing in Integers