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On Hamiltonian Bypasses in Digraphs satisfying Meyniel-like Condition
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On Hamiltonian Bypasses in Digraphs satisfying Meyniel-like Condition
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On Hamiltonian Bypasses in Digraphs satisfying Meyniel-like Condition
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Paper
On Hamiltonian Bypasses in Digraphs satisfying Meyniel-like Condition
2023
Overview
Let \\(G\\) be a strongly connected directed graph of order \\(p 3\\). In this paper, we show that if \\(d(x)+d(y) 2p-2\\) (respectively, \\(d(x)+d(y) 2p-1\\)) for every pair of non-adjacent vertices \\(x, y\\), then \\(G\\) contains a Hamiltonian path (with only a few exceptional cases that can be clearly characterized) in which the initial vertex dominates the terminal vertex (respectively, \\(G\\) contains two distinct verteces \\(x\\) and \\(y\\) such that there are two internally disjoint \\((x,y)\\)-paths of lengths \\(p-2\\) and \\(2\\)).
Publisher
Cornell University Library, arXiv.org
Subject
