Journal article Open Access

On the König deficiency of zero-reducible graphs

Miklós Bartha; Miklós Krész

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.

Files (621.9 kB)
Name Size
Bartha-Krész2019_Article_OnTheKönigDeficiencyOfZero-red.pdf
md5:5b369939d1da7dcd102a9eceb1ffdea5
621.9 kB Download
24
19
views
downloads
Views 24
Downloads 19
Data volume 11.8 MB
Unique views 24
Unique downloads 18

Share

Cite as