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The size ramsey number of graphs with bounded treewidth

Kamcev, Nina, Liebenau, Anita, Wood, David R. and Yepremyan, Liana (2021) The size ramsey number of graphs with bounded treewidth. SIAM Journal on Discrete Mathematics, 35 (1). 281 - 293. ISSN 0895-4801

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Identification Number: 10.1137/20M1335790


A graph G is Ramsey for a graph H if every 2-coloring of the edges of G contains a monochromatic copy of H. We consider the following question: If H has bounded treewidth, is there a sparse graph G that is Ramsey for H? Two notions of sparsity are considered. Firstly, we show that if the maximum degree and treewidth of H are bounded, then there is a graph G with O(| V (H)| ) edges that is Ramsey for H. This was previously only known for the smaller class of graphs H with bounded bandwidth. On the other hand, we prove that in general the treewidth of a graph G that is Ramsey for H cannot be bounded in terms of the treewidth of H alone. In fact, the latter statement is true even if the treewidth is replaced by the degeneracy and H is a tree.

Item Type: Article
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Additional Information: © 2021 Society for Industrial and Applied Mathematics.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 26 Apr 2022 14:57
Last Modified: 24 May 2024 04:27

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