id: 05844255
dt: j
an: 05844255
au: Chen, Bing; Zhang, Shenggui
ti: A new $σ_3$ type condition for heavy cycles in weighted graphs.
so: Ars Comb. 87, 393-402 (2008).
py: 2008
pu: Charles Babbage Research Centre, Winnipeg, MB
la: EN
cc: 
ut: weighted graph; weighted degree
ci: 
li: 
ab: Summary: A weighted graph is one in which every edge $e$ is assigned a
    nonnegative number $w(e)$, called the weight of $e$. The weight of a
    cycle is defined as the sum of the weights of its edges. The weighted
    degree of a vertex is the sum of the weights of the edges incident with
    it. In this paper, motivated by a recent result of J. Fujisawa, 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: { indent=6mm \item{(1)}the weighted degree sum of
    every three pairwise nonadjacent vertices is at least $m$; \item{(2)}in
    each induced claw and each induced modified claw of $G$ all edges have
    the same weight. This extends a theorem by S. Zhang, H. J. Broersma and
    X. Li. }
rv: