Component Games on Random Graphs

被引：0
|
作者：
Rani Hod
Michael Krivelevich
Tobias Müller
Alon Naor
Nicholas Wormald
机构：
[1] Tel Aviv University,School of Computer Science, Raymond and Beverly Sackler Faculty of Exact Sciences and Iby and Aladar Fleischman Faculty of Engineering
[2] Groningen University,Bernoulli Institute
[3] Tel Aviv University,School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences
[4] Monash University,School of Mathematics
来源：
Combinatorica | 2022年 / 42卷
关键词：
05C80; 91A24;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In the (1:b) component game played on a graph G, two players, Maker and Breaker, alternately claim 1 and b previously unclaimed edges of G, respectively. Maker’s aim is to maximise the size of a largest connected component in her graph, while Breaker is trying to minimise it. We show that the outcome of the game on the binomial random graph is strongly correlated with the appearance of a nonempty (b +2)-core in the graph.
引用
收藏
页码：1189 / 1229
页数：40
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