Vertex-disjoint cycles in bipartite tournaments

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• 作者：Diego Gonzá ; lez-Moreno^a ; ¹ ; ^{dgonzalez@correo.cua.uam.mx" class="auth_mail" title="E-mail the corresponding author} ; Camino Balbuena^b ; ^{m.camino.balbuena@upc.edu" class="auth_mail" title="E-mail the corresponding author} ; Mika Olsen^a ; ^{olsen@correo.cua.uam.mx" class="auth_mail" title="E-mail the corresponding author}
• 关键词：vertex-disjoint cycles ; bipartite tournament ; minimum degree
• 刊名：Electronic Notes in Discrete Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：54
• 期：Complete
• 页码：69-72
• 全文大小：161 K

文摘

Let k≥2$k\ge 2$ 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)≥2k−1${\delta }^{+}(D)\ge 2k-1$ contains at least k   vertex-disjoint cycles. In this work we prove that every bipartite tournament with minimum out-degree at least 2k−2$2k-2$ and minimum in-degree at least one contains k   vertex-disjoint cycles of length four, whenever k≥3$k\ge 3$. Finally, we show that every bipartite tournament with minimum degree at least (3k−1)/2$(3k-1)/2$ contains k vertex-disjoint cycles of length four.