Theoretical Computer Science ( IF 1.1 ) Pub Date : 2020-03-24 , DOI: 10.1016/j.tcs.2020.03.010 Jung-Heum Park , Hyeong-Seok Lim
Given disjoint source and sink sets, and , in a graph G, an unpaired k-disjoint path cover joining S and T is a set of pairwise vertex-disjoint paths that altogether cover every vertex of the graph, in which is a path from source to some sink . In terms of a generalized scattering number, named an r-scattering number, we characterize interval graphs that have an unpaired 2-disjoint path cover joining S and T for any possible configurations of source and sink sets S and T of size 2 each. Also, it is shown that the r-scattering number of an interval graph can be computed in polynomial time.
中文翻译:
不成对的2不相交路径可覆盖的区间图的特征
给定不相交的源和接收器集, 和 在图G中,连接S和T的不成对的k不相交路径覆盖是成对的顶点不相交路径的集合 总共覆盖了图的每个顶点,其中 是源头之路 到一些水槽 。在广义散射数量,名为方面R-散射数量,我们表征具有不成对2不相交的路径盖接合间隔的曲线图小号和Ť源和宿套任何可能的配置小号和Ť大小2各自的。而且,示出了可以以多项式时间来计算间隔图的r-散射数。