Weak and strong k-connectivity games

Asaf Ferber, Dan Hefetz

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)
135 Downloads (Pure)

Abstract

For a positive integer k, we consider the k-vertex-connectivity game, played on the edge set of Kn, the complete graph on n vertices. We first study the Maker–Breaker version of this game and prove that, for any integer k≥2 and sufficiently large n, Maker has a strategy to win this game within ⌊kn/2⌋+1 moves, which is easily seen to be best possible. This answers a question from Hefetz et al. (2009) [6]. We then consider the strong k-vertex-connectivity game. For every positive integer k and sufficiently large n, we describe an explicit first player’s winning strategy for this game.
Original languageEnglish
Pages (from-to)169-183
JournalEuropean Journal of Combinatorics
Volume35
Early online date4 Jul 2013
DOIs
Publication statusPublished - 1 Jan 2014

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