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Abstract:

The matching number of a graph is the maximum size of a set of vertex-disjoint edges. The transversal number is the minimum number of vertices needed to meet every edge. A graph has the König-Egerváry property if its matching number equals its transversal number. Lovász proved a characterization of graphs having the König-Egerváry property by means of forbidden subgraphs within graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovász's result to a characterization of all graphs having the König-Egerváry property in terms of forbidden configurations (which are certain arrangements of a subgraph and a maximum matching). In this work, we prove a characterization of graphs having the König-Egerváry property by means of forbidden subgraphs which is a strengthened version of the characterization by Korach et al. Using our characterization of graphs with the König-Egerváry property, we also prove a forbidden subgraph characterization for the class of edge-perfect graphs. © 2013 Elsevier B.V. All rights reserved.

Registro:

Documento: Artículo
Título:Forbidden subgraphs and the König-Egerváry property
Autor:Bonomo, F.; Dourado, M.C.; Durán, G.; Faria, L.; Grippo, L.N.; Safe, M.D.
Filiación:CONICET, Argentina
Departamento de Computación, FCEN, Universidad de Buenos Aires, Argentina
Instituto de Matemática, Universidade Federal Do Rio de Janeiro, Brazil
Instituto de Cálculo, FCEN, Universidad de Buenos Aires, Argentina
Departamento de Ingeniería Industrial, FCFM, Universidad de Chile, Chile
Departamento de Informática, IME, Universidade Do Estado Do Rio de Janeiro, Brazil
Instituto de Ciencias, Universidad Nacional de General Sarmiento, Argentina
Palabras clave:Edge-perfect graphs; Forbidden subgraphs; König-Egerváry graphs; König-Egerváry property; Maximum matching; Edge-perfect graphs; Forbidden configurations; Forbidden subgraph characterizations; Forbidden subgraphs; Matching numbers; Maximum matchings; Perfect matchings; Transversal number; Characterization; Graphic methods; Graph theory
Año:2013
Volumen:161
Número:16-17
Página de inicio:2380
Página de fin:2388
DOI: http://dx.doi.org/10.1016/j.dam.2013.04.020
Título revista:Discrete Applied Mathematics
Título revista abreviado:Discrete Appl Math
ISSN:0166218X
CODEN:DAMAD
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0166218X_v161_n16-17_p2380_Bonomo.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v161_n16-17_p2380_Bonomo

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Citas:

---------- APA ----------
Bonomo, F., Dourado, M.C., Durán, G., Faria, L., Grippo, L.N. & Safe, M.D. (2013) . Forbidden subgraphs and the König-Egerváry property. Discrete Applied Mathematics, 161(16-17), 2380-2388.
http://dx.doi.org/10.1016/j.dam.2013.04.020
---------- CHICAGO ----------
Bonomo, F., Dourado, M.C., Durán, G., Faria, L., Grippo, L.N., Safe, M.D. "Forbidden subgraphs and the König-Egerváry property" . Discrete Applied Mathematics 161, no. 16-17 (2013) : 2380-2388.
http://dx.doi.org/10.1016/j.dam.2013.04.020
---------- MLA ----------
Bonomo, F., Dourado, M.C., Durán, G., Faria, L., Grippo, L.N., Safe, M.D. "Forbidden subgraphs and the König-Egerváry property" . Discrete Applied Mathematics, vol. 161, no. 16-17, 2013, pp. 2380-2388.
http://dx.doi.org/10.1016/j.dam.2013.04.020
---------- VANCOUVER ----------
Bonomo, F., Dourado, M.C., Durán, G., Faria, L., Grippo, L.N., Safe, M.D. Forbidden subgraphs and the König-Egerváry property. Discrete Appl Math. 2013;161(16-17):2380-2388.
http://dx.doi.org/10.1016/j.dam.2013.04.020