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Winning Fast in Sparse Graph Construction Games

Published online by Cambridge University Press:  01 November 2008

OHAD N. FELDHEIM  and
MICHAEL KRIVELEVICH
OHAD N. FELDHEIM
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel (e-mail: [email protected]; [email protected])
MICHAEL KRIVELEVICH
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel (e-mail: [email protected]; [email protected])
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Abstract

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.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 6 , November 2008 , pp. 781 - 791
Copyright
Copyright © Cambridge University Press 2008

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