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Դարբինյան Սամվել Խ., Дарбинян Самвел Х.
Title:
On an Extension of the Ghouila-Houri Theorem
Other title:
Գուհիլա-Հուրիի թեորեմի մի ընդլայնման մասին ; Об одном расширении теоремы Гуйя-Ури
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Institute for Informatics and Automation Problems of NAS RA
Subject:
Mathematical cybernetics ; Computer science
Uncontrolled Keywords:
Digraphs ; 2-strong ; Hamiltonian-connected ; Hamiltonian cycles
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Abstract:
Let D be a 2-strong digraph of order n ≥ 8 such that for every vertex x ∈ V(D)\{z}, d(x) ≥ n and d(z) ≥ n − 4, where z is a vertex in V(D). We prove that: If D contains a cycle passing through z of length equal to n − 2, then D is Hamiltonian. We also give a new sufficient condition for a digraph to be Hamiltonian-connected.