publication . Article . Other literature type . 2019

On the König deficiency of zero-reducible graphs

Miklós Bartha; Miklós Krész;
Open Access
  • Published: 06 Nov 2019 Journal: Journal of Combinatorial Optimization (issn: 1382-6905, Copyright policy)
Abstract
<jats:title>Abstract</jats:title> <jats:p>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 <jats:italic>G</jats:italic> as the difference between the vertex covering number and the matching number of <jats:italic>G</jats:italic>. 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 defici...
Subjects
free text keywords: Graph matching, Independent set, König property, Graph reduction, Graph algorithm, Computational Theory and Mathematics, Control and Optimization, Applied Mathematics, Discrete Mathematics and Combinatorics, Computer Science Applications, Graph, Time complexity, Covering number, Matching (graph theory), Null graph, Combinatorics, Vertex (geometry), Mathematics
Funded by
EC| InnoRenew CoE
Project
InnoRenew CoE
Renewable materials and healthy environments research and innovation centre of excellence
  • Funder: European Commission (EC)
  • Project Code: 739574
  • Funding stream: H2020 | SGA-CSA
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