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

Text (20m1335790)
- Published Version
Download (406kB) |

## Abstract

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 |
---|---|

Official URL: | https://epubs.siam.org/journal/sjdmec |

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: | 07 Sep 2024 05:57 |

URI: | http://eprints.lse.ac.uk/id/eprint/114966 |

### Actions (login required)

View Item |