Winning fast in sparse graph construction games
ON Feldheim, M Krivelevich - Combinatorics, Probability and …, 2008 - cambridge.org
Combinatorics, Probability and Computing, 2008•cambridge.org
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.
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.
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.
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