On the König deficiency of zero-reducible graphs

Miklós Bartha () and Miklós Krész ()
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Miklós Bartha: Memorial University of Newfoundland
Miklós Krész: University of Szeged

Journal of Combinatorial Optimization, 2020, vol. 39, issue 1, No 16, 273-292

Abstract: Abstract 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 the matching number of G. 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 $$G-v$$G-v has a unique perfect matching is studied in connection with reduction.

Keywords: Graph matching; Independent set; König property; Graph reduction; Graph algorithm (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10878-019-00466-2

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