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A new sufficient condition for a 2-strong digraph to be Hamiltonian
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A new sufficient condition for a 2-strong digraph to be Hamiltonian
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Journal Article
A new sufficient condition for a 2-strong digraph to be Hamiltonian
2024
Overview
In this paper we prove the following new sufficient condition for a digraph to be Hamiltonian: ıt Let$D$be a 2-strong digraph of order$n\\geq 9$ . If$n-1$vertices of$D$have degrees at least$n+k$and the remaining vertex has degree at least$n-k-4$ , where$k$is a non-negative integer, then$D$is Hamiltonian. This is an extension of Ghouila-Houri's theorem for 2-strong digraphs and is a generalization of an early result of the author (DAN Arm. SSR (91(2):6-8, 1990). The obtained result is best possible in the sense that for$k=0$there is a digraph of order$n=8$(respectively,$n=9$ ) with the minimum degree$n-4=4$(respectively, with the minimum$n-5=4$ ) whose$n-1$vertices have degrees at least$n-1$ , but it is not Hamiltonian. We also give a new sufficient condition for a 3-strong digraph to be Hamiltonian-connected.
Publisher
Discrete Mathematics & Theoretical Computer Science
Subject
