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Trees with few leaves in tournaments
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Benford, Alistair and Montgomery, Richard (2022) Trees with few leaves in tournaments. Journal of Combinatorial Theory, Series B, 155 . pp. 141-170. doi:10.1016/j.jctb.2022.02.005 ISSN 0095-8956.
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Official URL: http://dx.doi.org/10.1016/j.jctb.2022.02.005
Abstract
We prove that there exists C>0 such that any (n+Ck)-vertex tournament contains a copy of every n-vertex oriented tree with k leaves, improving the previously best known bound of n+O(k2) vertices to give a result tight up to the value of C. Furthermore, we show that, for each k, there exists n0, such that, whenever n⩾n0, any (n+k−2)-vertex tournament contains a copy of every n-vertex oriented tree with at most k leaves, confirming a conjecture of Dross and Havet.
Item Type: | Journal Article | ||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||
Library of Congress Subject Headings (LCSH): | Trees (Graph theory), Tournaments (Graph theory) | ||||||||||
Journal or Publication Title: | Journal of Combinatorial Theory, Series B | ||||||||||
Publisher: | Elsevier | ||||||||||
ISSN: | 0095-8956 | ||||||||||
Official Date: | July 2022 | ||||||||||
Dates: |
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Volume: | 155 | ||||||||||
Page Range: | pp. 141-170 | ||||||||||
DOI: | 10.1016/j.jctb.2022.02.005 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||
Copyright Holders: | Elsevier | ||||||||||
Date of first compliant deposit: | 21 June 2022 | ||||||||||
Date of first compliant Open Access: | 2 March 2023 | ||||||||||
RIOXX Funder/Project Grant: |
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