2015/07/15 by Ferber, Asaf, Pfister, Pascal
#Combinatorics (math.CO) #Computer Science and Game Theory (cs.GT) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.1507.04229
In a strong game played on the edge set of a graph G there are two players, Red and Blue, alternating turns in claiming previously unclaimed edges of G (with Red playing first). The winner is the first one to claim all the edges of some target structure (such as a clique, a perfect matching, a Hamilton cycle, etc.). It is well known that Red can always ensure at least a draw in any strong game, but finding explicit winning strategies is a difficult and a quite rare task. We consider strong games played on the edge set of a random graph G ~ G(n,p) on n vertices. We prove, for sufficiently large n and a fixed constant 0 < p < 1, that Red can w.h.p win the perfect matching game on a random graph G ~ G(n,p).