November 6, 2019 Journal article Open Access

Miklós Bartha; Miklós Krész

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    <subfield code="a">König property</subfield>
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    <subfield code="u">Department of Computer Science, Memorial University of Newfoundland</subfield>
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    <subfield code="a">Miklós Bartha</subfield>
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    <subfield code="a">On the König deficiency of zero-reducible graphs</subfield>
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    <subfield code="a">&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;</subfield>
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