Ramsey games with giants
Combinatorics
2009-08-19 v2
Abstract
The classical result in the theory of random graphs, proved by Erdos and Renyi 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 the 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.
Keywords
Cite
@article{arxiv.0907.5590,
title = {Ramsey games with giants},
author = {Tom Bohman and Alan Frieze and Michael Krivelevich and Po-Shen Loh and Benny Sudakov},
journal= {arXiv preprint arXiv:0907.5590},
year = {2009}
}
Comments
29 pages; minor revisions