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
621.9 kB Download
Views 126
Downloads 116
Data volume 72.1 MB
Unique views 121
Unique downloads 114


Cite as