A sufficient condition for cyclability in directed graphs
نویسندگان
چکیده
منابع مشابه
An Implicit Degree Condition for Cyclability in Graphs
A vertex subset X of a graph G is said to be cyclable in G if there is a cycle in G containing all vertices of X. Ore [6] showed that the vertex set of G with cardinality n ≥ 3 is cyclable (i.e. G is hamiltonian) if the degree sum of any pair of nonadjacent vertices in G is at least n. Shi [8] and Ota [7] respectively generalized Ore’s result by considering the cyclability of any vertex subset ...
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The study of Hamiltonian graphs began with Dirac’s classic result in 1952. This was followed by that of Ore in 1960. In 1984 Fan generalized both these results with the following result: If G is a 2-connected graph of order n and max{d(u), d(v)}≥n/2 for each pair of vertices u and v with distance d(u, v)=2, then G is Hamiltonian. In 1991 Faudree–Gould–Jacobson–Lesnick proved that if G is a 2-co...
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Let G = (X, Y ; E) be a balanced 2-connected bipartite graph and S ⊂ V(G). We will say that S is cyclable in G if all vertices of S belong to a common cycle in G. We give sufficient degree conditions in a balanced bipartite graph G and a subset S ⊂ V(G) for the cyclability of the set S.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.11.066