Journal article Open Access

On the König deficiency of zero-reducible graphs

Miklós Bartha; Miklós Krész


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  <identifier identifierType="URL">https://zenodo.org/record/3532849</identifier>
  <creators>
    <creator>
      <creatorName>Miklós Bartha</creatorName>
      <nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0002-0996-8769</nameIdentifier>
      <affiliation>Department of Computer Science, Memorial University of Newfoundland</affiliation>
    </creator>
    <creator>
      <creatorName>Miklós Krész</creatorName>
      <affiliation>InnoRenew CoE; University of Primorska; University of Szeged</affiliation>
    </creator>
  </creators>
  <titles>
    <title>On the König deficiency of zero-reducible graphs</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2019</publicationYear>
  <subjects>
    <subject>Graph matching</subject>
    <subject>Independent set</subject>
    <subject>König property</subject>
    <subject>Graph reduction</subject>
    <subject>Graph algorithm</subject>
  </subjects>
  <dates>
    <date dateType="Issued">2019-11-06</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="issn">1382-6905</alternateIdentifier>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/3532849</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1007/s10878-019-00466-2</relatedIdentifier>
    <relatedIdentifier relatedIdentifierType="URL" relationType="IsPartOf">https://zenodo.org/communities/innorenew</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="https://creativecommons.org/licenses/by/4.0/legalcode">Creative Commons Attribution 4.0 International</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&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;</description>
  </descriptions>
  <fundingReferences>
    <fundingReference>
      <funderName>European Commission</funderName>
      <funderIdentifier funderIdentifierType="Crossref Funder ID">10.13039/501100000780</funderIdentifier>
      <awardNumber awardURI="info:eu-repo/grantAgreement/EC/H2020/739574/">739574</awardNumber>
      <awardTitle>Renewable materials and healthy environments research and innovation centre of excellence</awardTitle>
    </fundingReference>
  </fundingReferences>
</resource>
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