Opuscula Mathematica
Opuscula Math. 36, no. 3 (2016), 375-397

The hardness of the independence and matching clutter of a graph

Sasun Hambardzumyan
Vahan V. Mkrtchyan
Vahe L. Musoyan
Hovhannes Sargsyan
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.
Mathematics Subject Classification: 05C69, 05C70, 05C15.
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About the authors ▼
Sasun Hambardzumyan
Department of Informatics and Applied Mathematics, Yerevan State University, Yerevan, 0025, Armenia
Vahan V. Mkrtchyan
Institute for Informatics and Automation Problems, National Academy of Sciences of Republic of Armenia, 0014, Armenia
Vahe L. Musoyan
Stanford University, Computer Science Department, Stanford, CA 94305, USA
Hovhannes Sargsyan
Department of Informatics and Applied Mathematics, Yerevan State University, Yerevan, 0025, Armenia
About the article ▼
Communicated by Mariusz Meszka.
Received: 2014-03-30.
Revised: 2015-12-01.
Accepted: 2015-12-17.
Published online: 2016-02-21.
Cite this article as ▼
Sasun Hambardzumyan, Vahan V. Mkrtchyan, Vahe L. Musoyan, Hovhannes Sargsyan, The hardness of the independence and matching clutter of a graph, Opuscula Math. 36, no. 3 (2016), 375-397, http://dx.doi.org/10.7494/OpMath.2016.36.3.375.
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