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].
@article{bwmeta1.element.doi-10_7151_dmgt_1762,
author = {Junqing Cai and Hao Li and Wantao Ning},
title = {An Implicit Weighted Degree Condition For Heavy Cycles},
journal = {Discussiones Mathematicae Graph Theory},
volume = {34},
year = {2014},
pages = {801-810},
zbl = {1303.05106},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1762}
}
Junqing Cai; Hao Li; Wantao Ning. An Implicit Weighted Degree Condition For Heavy Cycles. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 801-810. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1762/
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