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Ramsey numbers of trails and circuits

Conlon, David and Tyomkyn, Mykhaylo (2022) Ramsey numbers of trails and circuits. Journal of Graph Theory . ISSN 0364-9024. doi:10.1002/jgt.22865. (In Press) https://resolver.caltech.edu/CaltechAUTHORS:20220726-997455000

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Abstract

We show that every two-colouring of the edges of the complete graph Kₙ contains a monochromatic trail or circuit of length at least 2n²/9+o(n²), which is asymptotically best possible.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1002/jgt.22865DOIArticle
https://arxiv.org/abs/2109.02633arXivDiscussion Paper
ORCID:
AuthorORCID
Conlon, David0000-0001-5899-1829
Additional Information:© 2022 Wiley Periodicals LLC. Version of Record online: 22 July 2022. Manuscript accepted: 27 June 2022. Manuscript revised: 19 April 2022. Manuscript received: 08 September 2021. Conlon was supported by NSF Award DMS-2054452 and Tyomkyn by ERC Synergy Grant DYNASNET 810115, the H2020-MSCA-RISE Project CoSP-GA No. 823748 and GACR Grant 19-04113Y.
Funders:
Funding AgencyGrant Number
NSFDMS-2054452
European Research Council (ERC)810115
European Research Council (ERC)823748
Grant Agency of the Czech Republic19-04113Y
Subject Keywords:Eulerian graphs; monochromatic components; Ramsey theory
DOI:10.1002/jgt.22865
Record Number:CaltechAUTHORS:20220726-997455000
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220726-997455000
Official Citation:Conlon, D. and Tyomkyn, M., Ramsey numbers of trails and circuits, J. Graph Theory. (2022), 1– 3. https://doi.org/10.1002/jgt.22865
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115854
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:27 Jul 2022 21:56
Last Modified:27 Jul 2022 21:56

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