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...
| Authors: | , , , , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2013 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/18841 |
| Online Access: | http://hdl.handle.net/11336/18841 |
| Access Level: | Open access |
| Keyword: | Edge-Perfect Graphs Forbidden Subgraphs König-Egerváry Property König-Egerváry Graphs Maximum Matching https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 https://purl.org/becyt/ford/1.2 |
| Summary: | 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. |
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