Biased orientation games

Ido Ben-Eliezer*, Michael Krivelevich, Benny Sudakov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study biased orientation games, in which the board is the complete graph K n, and OMaker (oriented maker) and OBreaker (oriented breaker) take turns in directing previously undirected edges of K n. At the end of the game, the obtained graph is a tournament. OMaker wins if the tournament has some property P and OBreaker wins otherwise. We provide bounds on the bias that is required for OMaker's win and for OBreaker's win in three different games. In the first game OMaker wins if the obtained tournament has a cycle. The second game is Hamiltonicity, where OMaker wins if the obtained tournament contains a Hamilton cycle. Finally, we consider the H-creation game, where OMaker wins if the obtained tournament has a copy of some fixed digraph H.

Original languageEnglish
Pages (from-to)1732-1742
Number of pages11
JournalDiscrete Mathematics
Issue number10
StatePublished - 28 May 2012


FundersFunder number
USA-Israel BSF1063/08, 2006322
USA-Israeli BSF
National Science FoundationDMS-0812005, DMS-1101185
European Research Council
Israel Science Foundation


    • Directed graphs
    • Hamiltonicity
    • Orientation games


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