Heavy cycles in k-connected weighted graphs with large weighted degree sums
نویسندگان
چکیده
منابع مشابه
Heavy Cycles in 2-Connected Weighted Graphs with Large Weighted Degree Sums
In this paper, we prove that a 2-connected weighted graph G contains either a Hamilton cycle or a cycle of weight at least 2m/3 if it satisfies the following conditions: (1) ∑3 i=1 d (vi) ≥ m, where v1, v2 and v3 are three pairwise nonadjacent vertices of G, and two of them are nonadjacent vertices of an induced claw or an induced modified claw; (2) In each induced claw and each induced modifie...
متن کاملHeavy cycles in weighted graphs
An (edge-)weighted graph is a graph in which each edge e is assigned a nonnegative real number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges, and an optimal cycle is one of maximum weight. The weighted degree w(v) of a vertex v is the sum of the weights of the edges incident with v. The following weighted analogue (and generalization) of a well-known...
متن کاملWeighted degrees and heavy cycles in weighted graphs
A weighted graph is a graph provided with an edge-weighting function w from the edge set to nonnegative real numbers. Bondy and Fan [Annals of Discrete Math. 41 (1989), 53– 69] began the study on the existence of heavy cycles in weighted graphs. Though several results with Dirac-type degree condition can be generalized to Ore-type one in unweighted graphs, it is shown in [Bondy et al., Discuss....
متن کاملAn Implicit Weighted Degree Condition for Heavy Cycles in Weighted Graphs
For a vertex v in a weighted graph G, id(v) denotes the implicit weighted degree of v. In this paper, we obtain the following result: Let G be a 2-connected weighted graph which satisfies the following conditions: (a) The implicit weighted degree sum of any three independent vertices is at least t; (b) w(xz) = w(yz) for every vertex z ∈ N(x) ∩ N(y) with xy / ∈ E(G); (c) In every triangle T of G...
متن کاملHeavy cycles in hamiltonian weighted graphs
Let G be a 2-connected weighted graph such that the minimum weighted degree is at least d. In [1], Bondy and Fan proved that either G contains a cycle of weight at least 2d or every heaviest cycle in G is a hamiltonian cycle. If G is not hamiltonian, this theorem implies the existence of a cycle of weight at least 2d, but in case of G is hamiltonian we cannot decide whether G has a heavy cycle ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.08.060