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Characterization of interval graphs that are unpaired 2-disjoint path coverable
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, S={s1,,sk} and T={t1,,tk}, in a graph G, an unpaired k-disjoint path cover joining S and T is a set of pairwise vertex-disjoint paths {P1,,Pk} that altogether cover every vertex of the graph, in which Pi is a path from source si to some sink tj. 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, 小号={s1个sķ}Ť={Ť1个Ťķ}在图G中,连接ST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{P1个Pķ} 总共覆盖了图的每个顶点,其中 P一世 是源头之路 s一世 到一些水槽 ŤĴ。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Ť源和宿套任何可能的配置小号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。

更新日期:2020-03-24
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