Strong games played on random graphs

• Main Authors: Ferber, Asaf (Contributor), Pfister, Pascal (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: European Mathematical Information Service (EMIS), 2017-06-19T15:06:48Z.
• Subjects: Article
• Online Access: Get fulltext

 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 K[subscript k], a perfect matching, a Hamilton cycle, etc.). In this paper we consider strong games played on the edge set of a random graph G ∼ G(n, p) on n vertices. We prove that G ∼ G(n, p) is typically such that Red can win the perfect matching game played on E(G), provided that p ∈ (0, 1) is a fixed constant.