Clique-perfectness and balancedness of some graph classes
Year: 2014
Type: article
Abstract: A graph is clique-perfect if the maximum size of a clique-independent set (a set of pairwise disjoint maximal cliques) and the minimum size of a clique-transversal set (a set of vertices meeting every maximal clique) coincide for each induced subgraph. A graph is balanced if its clique-matrix contains no square submatrix of odd size with exactly two ones per row and column. In this work, we give linear-time recognition algorithms and minimal forbidden induced subgraph characterizations of clique-perfectness and balancedness of P4-tidy graphs and a linear-time algorithm for computing a maximum clique-independent set and a minimum clique-transversal set for any P4-tidy graph. We also give a minimal forbidden induced subgraph characterization and a linear-time recognition algorithm for balancedness of paw-free graphs. Finally, we show that clique-perfectness of diamond-free graphs can be decided in polynomial time by showing that a diamond-free graph is clique-perfect if and only if it is balanced.
Institutions: Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad de Buenos Aires, University of Chile, National University of General Sarmiento, Instituto de Ciencias, Centre National de la Recherche Scientifique, Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes, Université Blaise Pascal
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2005131446