Título: Reducing graph transversals via edge contractions.
Palestrante: Vinícius Fernandes dos Santos, Universidade Federal de Minas Gerais.
Resumo: 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.
Obs. Joint work with Paloma T. Lima, Ignasi Sau and Uéverton S. Souza, available at arXiv:2005.01460.