AN IMPLICIT WEIGHTED DEGREE CONDITION FOR HEAVY CYCLES

作者：Cai, Junqing; Li, Hao^*; Ning, Wantao

来源：Discussiones Mathematicae - Graph Theory, 2014, 34(4): 801-810.

DOI：10.7151/dmgt.1762

• weighted graph
• hamiltonian cycles
• heavy cycles
• implicit degree
• implicit weighted degree

For a vertex v in a weighted graph G, id(w)(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 is an element of N(x) n N(y) with xy is not an element of E(C); (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].

• 出版日期2014
• 单位曲阜师范大学; 西安电子科技大学; 江汉大学