Ramsey games with giants

Tom Bohman*, Alan Frieze, Michael Krivelevich, Po Shen Loh, Benny Sudakov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The classical result in the theory of random graphs, proved by Erdos and Rényi in 1960, concerns the threshold for the appearance of the giant component in the random graph process. We consider a variant of this problem, with a Ramsey flavor. Now, each random edge that arrives in a sequence of rounds must be colored with one of r colors. The goal can be either to create a giant component in every color class, or alternatively, to avoid it in every color. One can analyze the offline or online setting for this problem. In this paper, we consider all these variants and provide nontrivial upper and lower bounds; in certain cases (like online avoidance) the obtained bounds are asymptotically tight.

Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalRandom Structures and Algorithms
Issue number1-2
StatePublished - Jan 2011


FundersFunder number
Directorate for Mathematical and Physical Sciences0753472, 0701183


    • Giant component
    • Ramsey game
    • Random graphs


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