In this paper we prove that Sweller has a strategy so that the Sweller-Start Competition-Independence game lasts at least (5n+3)/13 moves for every tree. Moreover, we show that there exist arbitrarily large trees such that the Sweller-Start Competition-Independence game lasts at most (5n+26)/12 moves, disproving a conjecture by Henning.
Cite
@article{arxiv.2303.09993,
title = {Bounds for the Competition-Independence game on trees},
author = {Jan Petr and Julien Portier},
journal= {arXiv preprint arXiv:2303.09993},
year = {2023}
}