A sufficient condition for pre-Hamiltonian cycles in bipartite digraphs

2017/06/01 by Darbinyan, Samvel Kh., Karapetyan, Iskandar A. · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.00233

Abstract

Let D be a strongly connected balanced bipartite directed graph of order 2a≥ 10 other than a directed cycle. Let x,y be distinct vertices in D. \x,y\ dominates a vertex z if x→ z and y→ z; in this case, we call the pair \x,y\ dominating. In this paper we prove: If max\d(x), d(y)\≥ 2a-2 for every dominating pair of vertices \x,y\, then D contains cycles of all lengths 2,4, … , 2a-2 or D is isomorphic to a certain digraph of order ten which we specify.

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• Sufficient conditions for a digraph to contain: a pre-Hamiltonian cycle and cycles of lengths 3 and 4

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