Opuscula Math. 36, no. 3 (2016), 375-397
http://dx.doi.org/10.7494/OpMath.2016.36.3.375

 
Opuscula Mathematica

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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  • 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
  • Communicated by Mariusz Meszka.
  • Received: 2014-03-30.
  • Revised: 2015-12-01.
  • Accepted: 2015-12-17.
  • Published online: 2016-02-21.
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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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