Theoretical Computer Science ( IF 0.9 ) Pub Date : 2021-03-10 , DOI: 10.1016/j.tcs.2021.03.012 Hans L. Bodlaender , Nick Brettell , Matthew Johnson , Giacomo Paesani , Daniël Paulusma , Erik Jan van Leeuwen
We consider the classical problems (Edge) Steiner Tree and Vertex Steiner Tree after restricting the input to some class of graphs characterized by a small set of forbidden induced subgraphs. We show a dichotomy for the former problem restricted to -free graphs and a dichotomy for the latter problem restricted to H-free graphs. We find that there exists an infinite family of graphs H such that Vertex Steiner Tree is polynomial-time solvable for H-free graphs, whereas there exist only two graphs H for which this holds for Edge Steiner Tree (assuming ). We also find that Edge Steiner Tree is polynomial-time solvable for -free graphs if and only if the treewidth of the class of -free graphs is bounded (subject to ). To obtain the latter result, we determine all pairs for which the class of -free graphs has bounded treewidth.
中文翻译:
用于遗传图类的Steiner树:树宽透视图
在将输入限制到以少量禁止诱导子图为特征的某些图类输入之后,我们考虑经典问题(边缘)斯坦纳树和顶点斯坦纳树。对于前一个问题,我们表现出二分法无图和对后者的二分法仅限于无H图。我们发现存在图H的无限家族,使得Vertex Steiner树对于无H图是多项式时间可解的,而对于Edge Steiner树只有两个图H(假设)。我们还发现Edge Steiner Tree是多项式时间可解的自由图形,当且仅当的类的树宽 自由图是有界的(以 )。为了获得后者的结果,我们确定所有对 对于该类 -自由图具有有限的树宽。