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Edge-disjoint Hamiltonian cycles in hypertournaments

✍ Scribed by Vojislav Petrovic; Carsten Thomassen

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 58 KB
Volume: 51
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20120

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✦ Synopsis

Abstract

We introduce a method for reducing k‐tournament problems, for k ≥ 3, to ordinary tournaments, that is, 2‐tournaments. It is applied to show that a k‐tournament on n ≥ k + 1 + 24__d__ vertices (when k ≥ 4) or on n ≥ 30__d__ + 2 vertices (when k = 3) has d edge‐disjoint Hamiltonian cycles if and only if it is d‐edge‐connected. Ironically, this is proved by ordinary tournament arguments although it only holds for k ≥ 3. We also characterizatize the pancyclic k‐tournaments, a problem posed by Gutin and Yeo.(Our characterization is slightly incomplete in that we prove it only for n large compared to k.). © 2005 Wiley Periodicals, Inc. J Graph Theory

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