Reducing graph transversals via edge contractions [article]

Paloma T. Lima, Vinicius F. dos Santos, Ignasi Sau, Uéverton S. Souza
2021 arXiv   pre-print
For a graph invariant π, the Contraction(π) problem consists in, given a graph G and two positive integers k,d, deciding whether one can contract at most k edges of G to obtain a graph in which π has dropped by at least d. Galby et al. [ISAAC 2019, MFCS 2019] recently studied the case where π is the size of a minimum dominating set. We focus on graph invariants defined as the minimum size of a vertex set that hits all the occurrences of graphs in a collection H according to a fixed containment
more » ... elation. We prove co-NP-hardness results under some assumptions on the graphs in H, which in particular imply that Contraction(π) is co-NP-hard even for fixed k=d=1 when π is the size of a minimum feedback vertex set or an odd cycle transversal. In sharp contrast, we show that when π is the size of a minimum vertex cover, the problem is in XP parameterized by d.
arXiv:2005.01460v2 fatcat:ieexjr6gv5ewvkgcqelgytsbf4