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Bounds for the Competition-Independence game on trees

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arxiv 2303.09993 v1 pith:DQJTE6ZV submitted 2023-03-17 math.CO

Jan Petr , Julien Portier This is my paper · ORCID
classification math.CO
keywords competition-independencegamelastsmovessweller-starttreesarbitrarilybounds
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abstract

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.

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