2013/04/15 by Clemens, Dennis, Ferber, Asaf, Glebov, Roman +2
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1304.4108
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.