Winning fast in sparse graph construction games

Ohad N. Feldheim; Michael Krivelevich

doi:10.1017/S0963548308009401

Winning fast in sparse graph construction games

Ohad N. Feldheim, Michael Krivelevich

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 > d¹¹2^2d+9n, then Maker can claim a copy of G in at most d¹¹2^2d+7n rounds. We also discuss a lower bound on the number of rounds Maker needs to win, and the gap between these bounds.

Original language	American English
Pages (from-to)	781-791
Number of pages	11
Journal	Combinatorics Probability and Computing
Volume	17
Issue number	6
DOIs	https://doi.org/10.1017/S0963548308009401
State	Published - Nov 2008
Externally published	Yes

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Winning fast in sparse graph construction games

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