Heavy Cycles in 2-Connected Weighted Graphs with Large Weighted Degree Sums

Authors:
Bing Chen;Shenggui Zhang;T. C. Cheng
Affiliations:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, P.R. China;Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, P.R. China and Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Ho ...;Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Venue:
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part III: ICCS 2007
Year:
2007

Citing 2
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A generalization of Fan's condition for Hamiltonicity, pancyclicity, and Hamiltonian connectedness

Discrete Mathematics
Graph Theory With Applications

Graph Theory With Applications

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Abstract

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) $\sum_{i=1}^3d^w(v_i)\ge m$, where v 1,v 2 and v 3 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 modified claw of G, all edges have the same weight. This extends several previous results on the existence of heavy cycles in weighted graphs.