Building spanning trees quickly in Maker-Breaker games
Combinatorics
2013-04-16 v1
Abstract
For a tree T on n vertices, we study the Maker-Breaker game, played on the edge set of the complete graph on n vertices, which Maker wins as soon as the graph she builds contains a copy of T. We prove that if T has bounded maximum degree, then Maker can win this game within n+1 moves. Moreover, we prove that Maker can build almost every tree on n vertices in n-1 moves and provide non-trivial examples of families of trees which Maker cannot build in n-1 moves.
Keywords
Cite
@article{arxiv.1304.4108,
title = {Building spanning trees quickly in Maker-Breaker games},
author = {Dennis Clemens and Asaf Ferber and Roman Glebov and Dan Hefetz and Anita Liebenau},
journal= {arXiv preprint arXiv:1304.4108},
year = {2013}
}