图的生成可圈性（英文）A Note on the Spanning Cyclability of Graphs
齐豪;艾尔肯·吾买尔;
摘要(Abstract)：
给定一个图G=(V,E)及其顶点集V的互不相交的非空子集A1,A2,···,Ar,如果存在互不相交的圈C1,C2,···,Cr满足Ai?V(Ci)(i=1,2,···,r)并且C1∪C2∪···∪Cr生成G,则称G是关于子集A1,A2,···,Ar生成可圈的.如果G关于V的任意r个互不相交的子集A1,A2,···,Ar都是生成可圈的,则称G是r-生成可圈的.进一步,如果G对于任意满足|A1∪A2∪···∪Ar|≤t的互不相交的点子集A1,A2,···,Ar是r-生成可圈的,则称G是阶数为t的r-生成可圈图.本文中,我们证明了:如果G是顶点数n≥3r+1,边数m≥(n-1)(n-2)2+k+r-2(r≥1,3≤k≤n-r+1)的图,则G是阶数为k+r-3的r-生成可圈图.本文将文献[1]中r=2的结果推广到了一般的情形.
关键词(KeyWords)： 哈密尔顿图;可圈性;生成可圈性
基金项目(Foundation): supported by NSFC(11361060)
作者(Author): 齐豪;艾尔肯·吾买尔;
Email:
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