Computing Subset Transversals in H-Free Graphs

2020/05/28 by Brettell, Nick, Johnson, Matthew, Paesani, Giacomo +1
#Combinatorics (math.CO) #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.13938

Abstract

We study the computational complexity of two well-known graph transversal problems, namely Subset Feedback Vertex Set and Subset Odd Cycle Transversal, by restricting the input to H-free graphs, that is, to graphs that do not contain some fixed graph~H as an induced subgraph. By combining known and new results, we determine the computational complexity of both problems on H-free graphs for every graph H except when H=sP₁+P₄ for some s≥ 1. As part of our approach, we introduce the Subset Vertex Cover problem and prove that it is polynomial-time solvable for (sP₁+P₄)-free graphs for every s≥ 1.

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