Journal article Open Access

On the König deficiency of zero-reducible graphs

Miklós Bartha; Miklós Krész


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        <foaf:name>Miklós Bartha</foaf:name>
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    <dct:title>On the König deficiency of zero-reducible graphs</dct:title>
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    <dcat:keyword>Graph matching</dcat:keyword>
    <dcat:keyword>Independent set</dcat:keyword>
    <dcat:keyword>König property</dcat:keyword>
    <dcat:keyword>Graph reduction</dcat:keyword>
    <dcat:keyword>Graph algorithm</dcat:keyword>
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    <dct:description>&lt;p&gt;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&amp;ouml;nig property is investigated in the context of reduction by introducing the K&amp;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&amp;ouml;nig deficiency of a graph is NP-complete even if we know that the graph reduces to the empty graph. Finally, the K&amp;ouml;nig deficiency of graphs G having a vertex v such that G &amp;minus; v has a unique perfect matching is studied in connection with reduction.&lt;/p&gt;</dct:description>
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