Vertex-disjoint directed cycles of prescribed length in tournaments with given minimum out-degree

2017/06/06 by Maoqun Wang, Weihua Yang, Wang, Maoqun +1
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1706.01699

openalex publication_date 2017/06/06 · openalex created_date 2017/06/15 · openalex updated_date 2026/07/28

Abstract

The Bermond-Thomassen conjecture states that, for any positive integer r, a digraph of minimum out-degree at least 2r-1 contains at least r vertex-disjoint directed cycles. In 2014, Bang-Jensen, Bessy and Thomass' e proved the conjecture for tournaments. In 2010, Lichiardopol conjectured that a tournament T with minimum out-degree at least (q-1)r-1 contains at least r vertex-disjoint q-cycles, where integer q≥3 and r≥1. In this paper, we address Lichiardopol's conjecture affirmatively. In particular, the case q=3 implies Bermond-Thomassen conjecture for tournaments.

Related

• Vertex-disjoint cycles in tournaments
• Note on Disjoint Cycles in Multipartite Tournaments
• Vertex-disjoint cycles of different lengths in tournaments
• Lichiardopol's conjecture on disjoint cycles in tournaments
• Two disjoint cycles in digraphs