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arXiv · 2504.21628

Cycles of lengths 3 and n-1 in digraphs under a Bang-Jensen-Gutin-Li type conditon

Zan-Bo Zhang·Wenhao Wu·Weihua He
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Abstract

Bang-Jensen-Gutin-Li type conditions are the conditions for hamiltonicity of digraphs which impose degree restrictions on nonadjacent vertices which have a common in-neighbor or a common out-neighbor. They can be viewed as an extension of Fan type conditions in undirected graphs, as well as generalization of locally (in-, out-)semicomplete digraphs. Since their first appearance in 1996, various Bang-Jensen-Gutin-Li type conditions for hamitonicity have come forth. In this paper we establish a condition of Bang-Jensen-Gutin-Li type which implies not only a hamiltonian cycle but also a 3-cycle and an (n-1)-cycle, with well-characterized exceptional graphs. We conjecture that this condition implies the existence of cycle of every length.

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Zan-Bo Zhang, Wenhao Wu, Weihua He. 2025-04-30. Cycles of lengths 3 and n-1 in digraphs under a Bang-Jensen-Gutin-Li type conditon. https://arxiv.org/abs/2504.21628

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