Hamiltonicity of locally hamiltonian and locally traceable graphs
نویسندگان
چکیده
منابع مشابه
Traceability of locally hamiltonian and locally traceable graphs
If P is a given graph property, we say that a graph G is locally P if 〈N(v)〉 has property P for every v ∈ V (G) where 〈N(v)〉 is the induced graph on the open neighbourhood of the vertex v. Pareek and Skupień (C. M. Pareek and Z. Skupień, On the smallest non-Hamiltonian locally Hamiltonian graph, J. Univ. Kuwait (Sci.), 10:9 17, 1983) posed the following two questions. Question 1 Is 9 the smalle...
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Let G be a graph. A Hamilton path in G is a path containing every vertex of G. The graph G is traceable if it contains a Hamilton path, while G is k-traceable if every induced subgraph of G of order k is traceable. In this paper, we study hamiltonicity of k-traceable graphs. For k ≥ 2 an integer, we define H(k) to be the largest integer such that there exists a k-traceable graph of order H(k) t...
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We state a sufficient condition for the square of a locally finite graph to contain a Hamilton circle, extending a result of Harary and Schwenk about finite graphs. We also give an alternative proof of an extension to locally finite graphs of the result of Chartrand and Harary that a finite graph not containing K4 or K2,3 as a minor is Hamiltonian if and only if it is 2-connected. We show furth...
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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.
متن کاملA sufficient condition for Hamiltonicity in locally finite graphs
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2018
ISSN: 0166-218X
DOI: 10.1016/j.dam.2017.10.030