计算机科学 ›› 2017, Vol. 44 ›› Issue (6): 94-96.doi: 10.11896/j.issn.1002-137X.2017.06.016
林政宽,赵源,樊建席,程宝雷
LIN Cheng-kuan, ZHAO Yuan, FAN Jian-xi and CHENG Bao-lei
摘要: 在计算机互连网络中,完全独立生成树在信息的可靠传输、并行传输、安全分发等方面具有重要的作用。假设图G中存在n棵生成树T1,T2,…,Tn,若对于图G中任意两个顶点u和v,满足u和v之间的路径在这n棵树中都是顶点不相交的,则称这n棵树为完全独立生成树(CISTs)。在2015年,Chang等人证明了对于包含n(n≥6)个顶点的任意图G,如果图G的最小顶点度数至少为n-2,那么,G中存在至少 n/3 棵CISTs[1]。在Chang等人的基础上,文中继续深入研究了图G中顶点度数和CISTs的棵数之间的关系。对于包含n(n≥5) 个顶点的任意图G,假设图G的最小顶点度数至少为n-2,得出度数为n-2的顶点的个数、度数为n-1的顶点的个数与图G中CISTs的棵数之间关系的推导等式,并证明了其正确性,从而改进了文献[1]中的结果。
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