Winning fast in sparse graph construction games

Ohad N. Feldheim, Michael Krivelevich

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


A graph construction game is a Maker-Breaker game. Maker and Breaker take turns in choosing previously unoccupied edges of the complete graph KN. Maker's aim is to claim a copy of a given target graph G while Breaker's aim is to prevent Maker from doing so. In this paper we show that if G is a d-degenerate graph on n vertices and N > d1122d+9n, then Maker can claim a copy of G in at most d1122d+7n rounds. We also discuss a lower bound on the number of rounds Maker needs to win, and the gap between these bounds.

Original languageAmerican English
Pages (from-to)781-791
Number of pages11
JournalCombinatorics Probability and Computing
Issue number6
StatePublished - Nov 2008
Externally publishedYes


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