Berger, Sören, Kohayakawa, Yoshiharu, Maesaka, Giulia Satiko, Martins, Taísa, Mendonça, Walner, Mota, Guilherme Oliveira and Parczyk, Olaf
(2021)
*The size-Ramsey number of powers of bounded degree trees.*
Journal of the London Mathematical Society, 103 (4).
1314 - 1332.
ISSN 0024-6107

Text (ramsey_trees-revised)
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## Abstract

Given a positive integer (Formula presented.), the (Formula presented.) -colour size-Ramsey number of a graph (Formula presented.) is the smallest integer (Formula presented.) such that there exists a graph (Formula presented.) with (Formula presented.) edges with the property that, in any colouring of (Formula presented.) with (Formula presented.) colours, there is a monochromatic copy of (Formula presented.). We prove that, for any positive integers (Formula presented.) and (Formula presented.), the (Formula presented.) -colour size-Ramsey number of the (Formula presented.) th power of any (Formula presented.) -vertex bounded degree tree is linear in (Formula presented.). As a corollary, we obtain that the (Formula presented.) -colour size-Ramsey number of (Formula presented.) -vertex graphs with bounded treewidth and bounded degree is linear in (Formula presented.), which answers a question raised by Kamčev, Liebenau, Wood and Yepremyan.

Item Type: | Article |
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Official URL: | https://londmathsoc.onlinelibrary.wiley.com/journa... |

Additional Information: | © 2020 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Date Deposited: | 10 Jan 2022 10:51 |

Last Modified: | 05 Oct 2024 03:24 |

URI: | http://eprints.lse.ac.uk/id/eprint/113369 |

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