Data: 29/10/2020, às 14:00 horas (GMT-3, horário de Brasília).
Título: Reducing graph transversals via edge contractions
Palestrante: Ignasi Sau (LIRMM, Université de Montpellier, CNRS)
Abstract: For a graph parameter $\pi$, the Contraction($\pi$) 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 $\pi$ has dropped by at least d. Galby et al. [ISAAC 2019, MFCS 2019] recently studied the case where $\pi$ is the size of a minimum dominating set. We focus on graph parameters 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 relation. We prove co-NP-hardness results under some assumptions on the graphs in H, which in particular imply that Contraction($\pi$) is co-NP-hard even for fixed k=d=1 when $\pi$ is the size of a minimum feedback vertex set or an odd cycle transversal. In sharp contrast, we show that when $\pi$ is the size of a minimum vertex cover, the problem is in XP parameterized by d.
Joint work with Paloma T. Lima, Vinicius F. dos Santos and Uéverton S. Souza, available at arXiv:2005.01460.