Published November 6, 2019 | Version v1
Journal article Open

On the König deficiency of zero-reducible graphs

  • 1. Department of Computer Science, Memorial University of Newfoundland
  • 2. InnoRenew CoE; University of Primorska; University of Szeged


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.



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InnoRenew CoE – Renewable materials and healthy environments research and innovation centre of excellence 739574
European Commission