On the proper interval completion problem within some chordal subclasses
Year: 2024
Type: article
Abstract: Given a property (graph class) Π, a graph G , and an integer k , the Π -completion problem consists of deciding whether we can turn G into a graph with the property Π by adding at most k edges to G . The Π-completion problem is known to be NP-hard for general graphs when Π is the property of being a proper interval graph (PIG). In this work, we study the PIG-completion problem within different subclasses of chordal graphs. We show that the problem remains NP-complete even when restricted to split graphs. We then turn our attention to positive results and present polynomial time algorithms to solve the PIG-completion problem when the input is restricted to caterpillar and threshold graphs. We also present an efficient algorithm for the minimum co-bipartite-completion for quasi-threshold graphs, which provides a lower bound for the PIG-completion problem within this graph class.
Source: Discrete Mathematics
Institutions: Centre National de la Recherche Scientifique, Université de Bordeaux, Laboratoire Bordelais de Recherche en Informatique, Institut Polytechnique de Bordeaux, University of Primorska, National University of General Sarmiento, Consejo Nacional de Investigaciones Científicas y Técnicas, National University of Rosario, University of Sheffield, Universidade Federal de Minas Gerais
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,120
Funders: Deutsche Forschungsgemeinschaft, Governo Brasil, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Javna Agencija za Raziskovalno Dejavnost RS, Fundação de Amparo à Pesquisa do Estado de Minas Gerais, Secretaria de Ciencia y Tecnica, Universidad de Buenos Aires, Secretaría de Ciencia y Técnica, Universidad de Buenos Aires
OpenAlex ID: W3205094627