Playing weighted Tron on Trees
Combinatorics
2014-12-15 v1 Discrete Mathematics
Abstract
We consider the weighted version of the Tron game on graphs where two players, Alice and Bob, each build their own path by claiming one vertex at a time, starting with Alice. The vertices carry non-negative weights that sum up to 1 and either player tries to claim a path with larger total weight than the opponent. We show that if the graph is a tree then Alice can always ensure to get at most 1/5 less than Bob, and that there exist trees where Bob can ensure to get at least 1/5 more than Alice.
Keywords
Cite
@article{arxiv.1412.4100,
title = {Playing weighted Tron on Trees},
author = {Daniel Hoske and Jonathan Rollin and Torsten Ueckerdt and Stefan Walzer},
journal= {arXiv preprint arXiv:1412.4100},
year = {2014}
}
Comments
10 pages, 5 figures