Journal article Open Access

On the König deficiency of zero-reducible graphs

Miklós Bartha; Miklós Krész

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  "description": "<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>", 
  "license": "", 
  "creator": [
      "affiliation": "Department of Computer Science, Memorial University of Newfoundland", 
      "@id": "", 
      "@type": "Person", 
      "name": "Mikl\u00f3s Bartha"
      "affiliation": "InnoRenew CoE; University of Primorska; University of Szeged", 
      "@type": "Person", 
      "name": "Mikl\u00f3s Kr\u00e9sz"
  "headline": "On the K\u00f6nig deficiency of zero-reducible graphs", 
  "image": "", 
  "datePublished": "2019-11-06", 
  "url": "", 
  "keywords": [
    "Graph matching", 
    "Independent set", 
    "K\u00f6nig property", 
    "Graph reduction", 
    "Graph algorithm"
  "@context": "", 
  "identifier": "", 
  "@id": "", 
  "@type": "ScholarlyArticle", 
  "name": "On the K\u00f6nig deficiency of zero-reducible graphs"
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