An Implicit Weighted Degree Condition For Heavy Cycles

Junqing Cai, Hao Li, and Wantao Ning. "An Implicit Weighted Degree Condition For Heavy Cycles." Discussiones Mathematicae Graph Theory 34.4 (2014): 801-810. <http://eudml.org/doc/269817>.

@article{JunqingCai2014,
abstract = {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].},
author = {Junqing Cai, Hao Li, Wantao Ning},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {weighted graph; hamiltonian cycles; heavy cycles; implicit degree; implicit weighted degree; Hamiltonian cycles},
language = {eng},
number = {4},
pages = {801-810},
title = {An Implicit Weighted Degree Condition For Heavy Cycles},
url = {http://eudml.org/doc/269817},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Junqing Cai
AU - Hao Li
AU - Wantao Ning
TI - An Implicit Weighted Degree Condition For Heavy Cycles
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 4
SP - 801
EP - 810
AB - 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].
LA - eng
KW - weighted graph; hamiltonian cycles; heavy cycles; implicit degree; implicit weighted degree; Hamiltonian cycles
UR - http://eudml.org/doc/269817
ER -