A Strategy for Isolator in the Toucher–Isolator Game on Trees

The Toucher–Isolator game was introduced recently by Dowden, Kang, Mikalački and Stojaković. Two players, Toucher Isolator, alternately claim an edge from a graph, where plays first. aims to touch as many vertices possible, Isolator minimize the number of that are so touched. Among trees with n vertices, they showed star is best choice for asked most suitable tree Toucher. Later, Räty answer path vertices. We give simple alternative proof this result. method determine should play breaking down gains losses in each move both players.