TY - GEN
T1 - On the parameterized complexity of simultaneous deletion problems
AU - Agrawal, Akanksha
AU - Krithika, R.
AU - Lokshtanov, Daniel
AU - Mouawad, Amer E.
AU - Ramanujan, M. S.
N1 - Publisher Copyright:
© Akanksha Agrawal, R. Krithika, Daniel Lokshtanov, Amer E. Mouawad, and M. S. Ramanujan.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - For a family of graphs F, an n-vertex graph G, and a positive integer k, the F-Deletion problem asks whether we can delete at most k vertices from G to obtain a graph in F. F-Deletion generalizes many classical graph problems such as Vertex Cover, Feedback Vertex Set, and Odd Cycle Transversal. A (multi) graph G = (V, ?ai=1Ei), where the edge set of G is partitioned into a color classes, is called an a-edge-colored graph. A natural extension of the F-Deletion problem to edge-colored graphs is the Simultaneous (F1, . . ., Fa)-Deletion problem. In the latter problem, we are given an a-edge-colored graph G and the goal is to find a set S of at most k vertices such that each graph Gi - S, where Gi = (V, Ei) and 1 = i = a, is in Fi. Recently, a subset of the authors considered the aforementioned problem with F1 = . . . = Fa being the family of all forests. They showed that the problem is fixed-parameter tractable when parameterized by k and a and can be solved in O(2O(ak)) time1. In this work, we initiate the investigation of the complexity of Simultaneous (F1, . . ., Fa)-Deletion with di erent families of graphs. In the process, we obtain a complete characterization of the parameterized complexity of this problem when one or more of the Fis is the class of bipartite graphs and the rest (if any) are forests. We show that if F1 is the family of all bipartite graphs and each of F2 = F3 = . . . = Fa is the family of all forests then the problem is fixed-parameter tractable parameterized by k and a. However, even when F1 and F2 are both the family of all bipartite graphs, then the Simultaneous (F1, F2)-Deletion problem itself is already W[1]-hard.
AB - For a family of graphs F, an n-vertex graph G, and a positive integer k, the F-Deletion problem asks whether we can delete at most k vertices from G to obtain a graph in F. F-Deletion generalizes many classical graph problems such as Vertex Cover, Feedback Vertex Set, and Odd Cycle Transversal. A (multi) graph G = (V, ?ai=1Ei), where the edge set of G is partitioned into a color classes, is called an a-edge-colored graph. A natural extension of the F-Deletion problem to edge-colored graphs is the Simultaneous (F1, . . ., Fa)-Deletion problem. In the latter problem, we are given an a-edge-colored graph G and the goal is to find a set S of at most k vertices such that each graph Gi - S, where Gi = (V, Ei) and 1 = i = a, is in Fi. Recently, a subset of the authors considered the aforementioned problem with F1 = . . . = Fa being the family of all forests. They showed that the problem is fixed-parameter tractable when parameterized by k and a and can be solved in O(2O(ak)) time1. In this work, we initiate the investigation of the complexity of Simultaneous (F1, . . ., Fa)-Deletion with di erent families of graphs. In the process, we obtain a complete characterization of the parameterized complexity of this problem when one or more of the Fis is the class of bipartite graphs and the rest (if any) are forests. We show that if F1 is the family of all bipartite graphs and each of F2 = F3 = . . . = Fa is the family of all forests then the problem is fixed-parameter tractable parameterized by k and a. However, even when F1 and F2 are both the family of all bipartite graphs, then the Simultaneous (F1, F2)-Deletion problem itself is already W[1]-hard.
KW - Edge-colored graphs
KW - Feedback vertex set
KW - Odd cycle transversal
KW - Parameterized complexity
KW - Simultaneous deletion
UR - http://www.scopus.com/inward/record.url?scp=85043991960&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.FSTTCS.2017.9
DO - 10.4230/LIPIcs.FSTTCS.2017.9
M3 - Conference contribution
AN - SCOPUS:85043991960
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017
A2 - Lokam, Satya
A2 - Ramanujam, R.
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017
Y2 - 12 December 2017 through 14 December 2017
ER -