Edge deletion to tree-like graph classes

• Autores: Koch, Ivo Valerio; Pardal, Nina; Fernandes Dos Santos, Vinicius
• Año de publicación: 2024
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: EDGE DELETION PROBLEMS; MODIFICATION PROBLEMS; SPARSE GRAPH CLASSES
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

For a fixed property (graph class) Π, given a graph G and an integer k, the Π-deletion problem consists in deciding if we can turn G into a graph with the property Π by deleting at most k edges. The Π-deletion problem is known to be NP-hard for most of the well-studied graph classes, such as chordal, interval, bipartite, planar, comparability and permutation graphs, among others; even deletion to cacti is known to be NP-hard for general graphs. However, there is a notable exception: the deletion problem to trees is polynomial. Motivated by this fact, we study the deletion problem for some classes similar to trees, addressing in this way a knowledge gap in the literature. We prove that deletion to cacti is hard even when the input is a bipartite graph. On the positive side, we show that the problem becomes tractable when the input is chordal, and for the special case of quasi-threshold graphs we give a simpler and faster algorithm. In addition, we present sufficient structural conditions on the graph class Π that imply the NP-hardness of the Π-deletion problem, and show that deletion from general graphs to some well-known subclasses of forests is NP-hard.
Fil: Koch, Ivo Valerio. Universidad Nacional de General Sarmiento; Argentina
Fil: Pardal, Nina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina
Fil: Fernandes Dos Santos, Vinicius. Universidade Federal de Minas Gerais; Brasil