Forbidden subgraphs and the König-Egerváry property
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...
| Autores: | , , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | Argentina |
| Institución: | Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| Repositorio: | Biblioteca Digital (UBA-FCEN) |
| Idioma: | inglés |
| OAI Identifier: | paperaa:paper_0166218X_v161_n16-17_p2380_Bonomo |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0166218X_v161_n16-17_p2380_Bonomo |
| Access Level: | acceso abierto |
| Palabra clave: | Edge-perfect graphs Forbidden subgraphs König-Egerváry graphs König-Egerváry property Maximum matching Forbidden configurations Forbidden subgraph characterizations Matching numbers Maximum matchings Perfect matchings Transversal number Characterization Graphic methods Graph theory |
| Sumario: | 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. |
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