An efficient condition for a graph to be Hamiltonian
نویسندگان
چکیده
LetG= (V ,E) be a 2-connected simple graph and let dG(u, v) denote the distance between two vertices u, v in G. In this paper, it is proved: if the inequality dG(u) + dG(v) |V (G)| − 1 holds for each pair of vertices u and v with dG(u, v) = 2, then G is Hamiltonian, unless G belongs to an exceptional class of graphs. The latter class is described in this paper. Our result implies the theorem of Ore [Note on Hamilton circuits, Amer. Math. Monthly 67 (1960) 55]. However, it is not included in the theorem of Fan [New sufficient conditions for cycles in graph, J. Combin. Theory Ser. B 37 (1984) 221–227]. © 2007 Elsevier B.V. All rights reserved. MSC: 05C12; 05C45
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عنوان ژورنال:
- Discrete Applied Mathematics
دوره 155 شماره
صفحات -
تاریخ انتشار 2007