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.
Computing Subset Transversals in H-Free Graphs / Brettell, N.; Johnson, M.; Paesani, G.; Paulusma, D.. - 12301:(2020), pp. 187-199. ( International Workshop on Graph-Theoretic Concepts in Computer Science Leeds, Regno Unito ) [10.1007/978-3-030-60440-0_15].
Computing Subset Transversals in H-Free Graphs
Paesani G.;
2020
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
