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", 
    "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>", 
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    "title": "On the K\u00f6nig deficiency of zero-reducible graphs", 
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      "title": "Journal of Combinatorial Optimization"
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    "keywords": [
      "Graph matching", 
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    "publication_date": "2019-11-06", 
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        "affiliation": "Department of Computer Science, Memorial University of Newfoundland", 
        "name": "Mikl\u00f3s Bartha"
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