@Article{Hambardzumyan2016,
author = "Hambardzumyan, Sasun and Mkrtchyan, Vahan V. and Musoyan, Vahe L. and Sargsyan, Hovhannes",
title = "The hardness of the independence and matching clutter of a graph",
journal = "Opuscula Math.",
year = "2016",
volume = "36",
number = "3",
pages = "375--397",
doi = "http://dx.doi.org/10.7494/OpMath.2016.36.3.375",
url = "http://dx.doi.org/10.7494/OpMath.2016.36.3.375",
abstract = "A clutter (or antichain or Sperner family) \(L\) is a pair \((V,E)\), where \(V\) is a finite set and \(E\) is a family of subsets of \(V\) none of which is a subset of another. Usually, the elements of \(V\) are called vertices of \(L\), and the elements of \(E\) are called edges of \(L\). A subset \(s_e\) of an edge \(e\) of a clutter is called recognizing for \(e\), if \(s_e\) is not a subset of another edge. The hardness of an edge \(e\) of a clutter is the ratio of the size of \(e\)'s smallest recognizing subset to the size of \(e\). The hardness of a clutter is the maximum hardness of its edges. We study the hardness of clutters arising from independent sets and matchings of graphs.",
keywords = "clutter, hardness, independent set, maximal independent set, matching, maximal matching",
issn = "1232-9274"
}