Sufficient condition for Hamiltonicity of N2-locally connected claw-free graphs
نویسندگان
چکیده
منابع مشابه
Hamiltonian N2-locally connected claw-free graphs
A graph G is N2-locally connected if for every vertex v in G, the edges not incident with v but having at least one end adjacent to v in G induce a connected graph. In 1990, Ryjác̆ek conjectured that every 3-connected N2-locally connected claw-free graph is hamiltonian. This conjecture is proved in this note.
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Among the well-known sufficient degree conditions for the Hamiltonicity of a finite graph, the condition of Asratian and Khachatrian is the weakest and thus gives the strongest result. Diestel conjectured that it should extend to locally finite infinite graphs G, in that the same condition implies that the Freudenthal compactification of G contains a circle through all its vertices and ends. We...
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Kuipers and Veldman conjectured that any 3-connected claw-free graph with order ν and minimum degree δ ≥ ν+6 10 is Hamiltonian for ν sufficiently large. In this paper, we prove that if H is a 3-connected claw-free graph with sufficiently large order ν, and if δ(H) ≥ ν+5 10 , then either H is hamiltonian, or δ(H) = ν+5 10 and the Ryjác̆ek’s closure cl(H) of H is the line graph of a graph obtained...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00163-6