Journal article Open Access

# On the König deficiency of zero-reducible graphs

Miklós Bartha; Miklós Krész

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<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:creator>Miklós Bartha</dc:creator>
<dc:creator>Miklós Krész</dc:creator>
<dc:date>2019-11-06</dc:date>
<dc:description>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 König property is investigated in the context of reduction by introducing the König 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 König deficiency of a graph is NP-complete even if we know that the graph reduces to the empty graph. Finally, the König deficiency of graphs G having a vertex v such that G − v has a unique perfect matching is studied in connection with reduction.</dc:description>
<dc:identifier>https://zenodo.org/record/3532849</dc:identifier>
<dc:identifier>10.1007/s10878-019-00466-2</dc:identifier>
<dc:identifier>oai:zenodo.org:3532849</dc:identifier>
<dc:relation>info:eu-repo/grantAgreement/EC/H2020/739574/</dc:relation>
<dc:relation>info:eu-repo/semantics/altIdentifier/issn/1382-6905</dc:relation>
<dc:relation>url:https://zenodo.org/communities/innorenew</dc:relation>
<dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
<dc:source>Journal of Combinatorial Optimization</dc:source>
<dc:subject>Graph matching</dc:subject>
<dc:subject>Independent set</dc:subject>
<dc:subject>König property</dc:subject>
<dc:subject>Graph reduction</dc:subject>
<dc:subject>Graph algorithm</dc:subject>
<dc:title>On the König deficiency of zero-reducible graphs</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
<dc:type>publication-article</dc:type>
</oai_dc:dc>

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