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- W600528036 abstract "An edge of G is singular if it does not lie on any triangle of G; otherwise, it is non-singular. A vertex u of a graph G is called locally connected if the induced subgraph G[N(u)] by its neighborhood is connected; otherwise, it is called locally disconnected. In this paper, we prove that if a connected claw-free graph G of order at least three satisfies the following two conditions: For each locally disconnected vertex v of G with degree at least 3, there is a nonnegative integer s such that v lies on an induced cycle of length at least 4 with at most s non-singular edges and with at least s−3 locally connected vertices; for each locally disconnected vertex v of G with degree 2, there is a nonnegative integer s such that v lies on an induced cycle C with at most s non-singular edges and with at least s−2 locally connected vertices and such that the subgraph induced by those vertices of C that have degree two in G is a path or a cycle, then G is Hamiltonian, and it is best possible in some sense. Our result is a common extension of two known results in Bielak (2000) and in Li (2002); hence also of the results in Oberly and Sumner (1979) and in Ryjáček (1990)." @default.
- W600528036 created "2016-06-24" @default.
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- W600528036 date "2015-11-01" @default.
- W600528036 modified "2023-09-24" @default.
- W600528036 title "Hamiltonian claw-free graphs with locally disconnected vertices" @default.
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- W600528036 doi "https://doi.org/10.1016/j.disc.2015.04.020" @default.
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