Cycles in Weighted Graphs
Bian Qiu · 2003
Proves the following result:suppose G is a 2-connected weighted graph that satisfies for any independent set S={u,v,w},there exists x≠y∈S such that dw(x)+dw(y)≥m,then there exists a Hamilton cycle or a cycle of weight at least m.This generalizes related theroems on the existence of long cycles in unweighted graphs to weighted graphs and the related result in weighted graphs.