%0 Journal Article %T k-连通图中最长圈上可收缩边的数目<br>On the number of contractible edges of longest cycles in k-connected graphs %A 王珊珊 %A 齐恩凤< %A br> %A WANG Shan-shan %A QI En-feng %J 山东大学学报(理学版) %D 2015 %R 10.6040/j.issn.1671-9352.0.2015.072 %X 摘要: 给出了k-连通图中最长圈上的可收缩边的数目,得到如下结果:任意断片的阶至少为「k/2+1 的k-连通图中最长圈上至少有3 条可收缩边;更进一步,若该k-连通图中存在哈密顿圈,则哈密顿圈上至少有6 条可收缩边。<br>Abstract: The number of contractible edges of longest cycles in k-connected graphs is given. The conclusions are that if every fragment of a k-connected graph has an order at least 「k/2+1,then there exist at least three contractible edges on the longest cycle of this graph. Furthermore, if this graph has a hamiltonian cycle, then there exist at least six contractible edges on the hamiltonian cycle %K 最长圈 %K 可收缩边 %K < %K em> %K k< %K /em> %K -连通图 %K 哈密顿圈 %K < %K br> %K contractible edge %K hamiltonian cycle %K < %K em> %K k< %K /em> %K -connected graph %K longest cycle %U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2015.072