Three early problems on size Ramsey numbers
Abstract
The size Ramsey number of a graph is defined as the minimum number of edges in a graph such that there is a monochromatic copy of in every two-coloring of . The size Ramsey number was introduced by Erd\H{o}s, Faudree, Rousseau, and Schelp in 1978 and they ended their foundational paper by asking whether one can determine up to a constant factor the size Ramsey numbers of three families of graphs: complete bipartite graphs, book graphs (obtained by adding many common neighbors to the vertices of a clique), and starburst graphs (obtained by adding many pendant edges to each vertex of a clique). In this paper, we completely resolve the latter two questions and make substantial progress on the first by determining the size Ramsey number of up to a constant factor for all .
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Cite
@article{arxiv.2111.05420,
title = {Three early problems on size Ramsey numbers},
author = {David Conlon and Jacob Fox and Yuval Wigderson},
journal= {arXiv preprint arXiv:2111.05420},
year = {2023}
}
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23 pages