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Vertex-disjoint cycles in bipartite tournaments.

Authors :
González-Moreno, Diego
Balbuena, Camino
Olsen, Mika
Source :
Electronic Notes in Discrete Mathematics; Oct2016, Vol. 54, p69-72, 4p
Publication Year :
2016

Abstract

Let k ≥ 2 be an integer. Bermond and Thomassen [Bermond J. C., Thomassen, C., Cycles in digraphs a survey, Journal of Graph Theory 5(1) (1981) 1–43] conjectured that every digraph D with δ + ( D ) ≥ 2 k − 1 contains at least k vertex-disjoint cycles. In this work we prove that every bipartite tournament with minimum out-degree at least 2 k − 2 and minimum in-degree at least one contains k vertex-disjoint cycles of length four, whenever k ≥ 3 . Finally, we show that every bipartite tournament with minimum degree at least ( 3 k − 1 ) / 2 contains k vertex-disjoint cycles of length four. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
15710653
Volume :
54
Database :
Supplemental Index
Journal :
Electronic Notes in Discrete Mathematics
Publication Type :
Academic Journal
Accession number :
118739664
Full Text :
https://doi.org/10.1016/j.endm.2016.09.013