Journal article Open Access

# On the König deficiency of zero-reducible graphs

Miklós Bartha; Miklós Krész

### Citation Style Language JSON Export

{
"DOI": "10.1007/s10878-019-00466-2",
"container_title": "Journal of Combinatorial Optimization",
"title": "On the K\u00f6nig deficiency of zero-reducible graphs",
"issued": {
"date-parts": [
[
2019,
11,
6
]
]
},
"abstract": "<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 K&ouml;nig property is investigated in the context of reduction by introducing the K&ouml;nig 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 K&ouml;nig deficiency of a graph is NP-complete even if we know that the graph reduces to the empty graph. Finally, the K&ouml;nig deficiency of graphs G having a vertex v such that G &minus; v has a unique perfect matching is studied in connection with reduction.</p>",
"ISSN": "1382-6905",
"author": [
{
"family": "Mikl\u00f3s Bartha"
},
{
"family": "Mikl\u00f3s Kr\u00e9sz"
}
],
"type": "article-journal",
"id": "3532849"
}
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