Highly linked tournaments
Pokrovskiy, Alexey (2015) Highly linked tournaments. Journal of Combinatorial Theory, Series B 115 , pp. 339-347. ISSN 0095-8956.
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Abstract
A (possibly directed) graph is k-linked if for any two disjoint sets of vertices {x1,…,xk} and {y1,…,yk} there are vertex disjoint paths P1,…,Pk such that Pi goes from xi to yi. A theorem of Bollobás and Thomason says that every 22k-connected (undirected) graph is k-linked. It is desirable to obtain analogues for directed graphs as well. Although Thomassen showed that the Bollobás-Thomason Theorem does not hold for general directed graphs, he proved an analogue of the theorem for tournaments - there is a function f(k) such that every strongly f(k)-connected tournament is k-linked. The bound on f(k) was reduced to O(klogk) by Kühn, Lapinskas, Osthus, and Patel, who also conjectured that a linear bound should hold. We prove this conjecture, by showing that every strongly 452k-connected tournament is k-linked.
Metadata
| Item Type: | Article |
|---|---|
| Keyword(s) / Subject(s): | Connectivity of tournaments, Linkedness, Linkage structures |
| School: | Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics |
| Depositing User: | Alexey Pokrovskiy |
| Date Deposited: | 21 Jan 2019 15:44 |
| Last Modified: | 26 Jul 2019 22:03 |
| URI: | http://eprints.bbk.ac.uk/id/eprint/25897 |
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