Journal article Open Access

On the König deficiency of zero-reducible graphs

Miklós Bartha; Miklós Krész


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{
  "DOI": "10.1007/s10878-019-00466-2", 
  "container_title": "Journal of Combinatorial Optimization", 
  "title": "On the K\u00f6nig deficiency of zero-reducible graphs", 
  "issued": {
    "date-parts": [
      [
        2019, 
        11, 
        6
      ]
    ]
  }, 
  "abstract": "<p>A confluent and terminating reduction system is introduced for graphs,which preserves the number of their perfect matchings. A union-find algorithm is presented to carry out reduction in almost linear time. The K&ouml;nig property is investigated in the context of reduction by introducing the K&ouml;nig deficiency of a graph G as the difference between the vertex covering number and thematching number ofG. It is shown that the problem of finding the K&ouml;nig deficiency of a graph is NP-complete even if we know that the graph reduces to the empty graph. Finally, the K&ouml;nig deficiency of graphs G having a vertex v such that G &minus; v has a unique perfect matching is studied in connection with reduction.</p>", 
  "ISSN": "1382-6905", 
  "author": [
    {
      "family": "Mikl\u00f3s Bartha"
    }, 
    {
      "family": "Mikl\u00f3s Kr\u00e9sz"
    }
  ], 
  "type": "article-journal", 
  "id": "3532849"
}
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