since 1980, many graph theorists such as j . a . bondy, b . bollobas, h . j . broersma and fan genghua etc . have been studying the existence of heavy cycles in weighted graphs and gained a lot of important results broersma以及范更華等開始研究賦權(quán)圖中重圈的存在性,得到了許多重要的結(jié)論。