Decomposing tournaments into paths

Lo, Allan, Patel, Viresh, Skokan, Jozef ORCID: 0000-0003-3996-7676 and Talbot, John (2020) Decomposing tournaments into paths. Proceedings of the London Mathematical Society, 121 (2). 426 - 461. ISSN 0024-6115

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Abstract

We consider a generalisation of Kelly's conjecture which is due to Alspach, Mason, and Pullman from 1976. Kelly's conjecture states that every regular tournament has an edge decomposition into Hamilton cycles, and this was proved by Kühn and Osthus for large tournaments. The conjecture of Alspach, Mason, and Pullman asks for the minimum number of paths needed in a path decomposition of a general tournament T . There is a natural lower bound for this number in terms of the degree sequence of T and it is conjectured that this bound is correct for tournaments of even order. Almost all cases of the conjecture are open and we prove many of them.

Item Type:	Article
Official URL:	https://www.lms.ac.uk/publications/plms
Additional Information:	© 2020 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	19 Dec 2019 10:48
Last Modified:	12 Dec 2024 02:01
URI:	http://eprints.lse.ac.uk/id/eprint/102950

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