TY - JOUR
T1 - Winning fast in sparse graph construction games
AU - Feldheim, Ohad N.
AU - Krivelevich, Michael
PY - 2008/11
Y1 - 2008/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=54849442251&partnerID=8YFLogxK
U2 - 10.1017/S0963548308009401
DO - 10.1017/S0963548308009401
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AN - SCOPUS:54849442251
SN - 0963-5483
VL - 17
SP - 781
EP - 791
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
IS - 6
ER -