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An Implicit Weighted Degree Condition For Heavy Cycles

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Cai J., Li H., Ning W.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 4

801-810

For a vertex v in a weighted graph G, idw(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, either all edges of T have different weights or all edges of T have the same weight. Then G contains either a hamiltonian cycle or a cycle of weight at least 2t/3. This generalizes the result of Zhang et al. [9].

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Cai J.

1 Li H.

1 Ning W.

1 2014

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An Implicit Weighted Degree Condition For Heavy Cycles