Given a simple graph G, a set (Formula presented.) is a neighborhood cover set if every edge and vertex of G belongs to some G[v] with (Formula presented.), where G[v] denotes the subgraph of G induced by the closed neighborhood of the vertex v. Two elements of (Formula presented.) are neighborhood-independent if there is no vertex (Formula presented.) such that both elements are in G[v]. A set (Formula presented.) is neighborhood-independent if every pair of elements of S is neighborhood-independent. Let (Formula presented.) be the size of a minimum neighborhood cover set and (Formula presented.) of a maximum neighborhood-independent set. Lehel and Tuza defined neighborhood-perfect graphs G as those where the equality (Formula presented.) holds for every induced subgraph (Formula presented.) of G. In this work we prove forbidden induced subgraph characterizations of the class of neighborhood-perfect graphs, restricted to two superclasses of cographs: (Formula presented.)-tidy graphs and tree-cographs. We give as well linear-time algorithms for solving the recognition problem of neighborhood-perfect graphs and the problem of finding a minimum neighborhood cover set and a maximum neighborhood-independent set in these same classes. Finally we prove that although for complements of trees finding these optimal sets can be achieved in linear-time, for complements of bipartite graphs it is (Formula presented.)-hard. © 2017 Springer Science+Business Media, LLC, part of Springer Nature
Documento: | Artículo |
Título: | Neighborhood covering and independence on P4-tidy graphs and tree-cographs |
Autor: | Durán, G.; Safe, M.; Warnes, X. |
Filiación: | Instituto de Cálculo and Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina Departamento de Ingeniería Industrial, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile Buenos Aires, Argentina Departamento de Matemática, Universidad Nacional del Sur, Bahía Blanca, Argentina Graduate School of Business, Stanford University, Stanford, CA, United States |
Palabras clave: | $$P_4$$P4-tidy graphs; Co-bipartite graphs; Forbidden induced subgraphs; Neighborhood-perfect graphs; Recognition algorithms; Tree-cographs |
Año: | 2017 |
Página de inicio: | 1 |
Página de fin: | 32 |
DOI: | http://dx.doi.org/10.1007/s10479-017-2712-z |
Título revista: | Annals of Operations Research |
Título revista abreviado: | Ann. Oper. Res. |
ISSN: | 02545330 |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02545330_v_n_p1_Duran |