Bounds for the Competition-Independence game on trees

In this paper we prove that Sweller has a strategy so that the Sweller-Start Competition-Independence game lasts at least $(5n+3)\mathrm{/}13$ moves for every tree. Moreover, we show that there exist arbitrarily large trees such that the Sweller-Start Competition-Independence game lasts at most $(5n+26)\mathrm{/}12$ moves, disproving a conjecture by Henning.