A lower bound on the independence number of arbitrary hypergraphs

  • Authors:

  • Torsten Thiele

  • Affiliations:

  • Courant Institute, New York University, New York, NY and Freie Universität Berlin, Berlin, Germany

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 1999

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Abstract

We present a lower bound on the independence number of arbitraryhypergraphs in terms of the degree vectors. The degree vector of avertex v is given by d(v) =(d1(v), d2(v),…) where dm(v) is the number ofedges of size m containing v. We define a functionf with the property that any hypergraph H =(V, E) satisfies α(H) ≥ΣvεVf(d(v)). This lower bound is sharp whenH is a match, and it generalizes known bounds of Caro-Weiand Caro-Tuza for ordinary graphs and uniform hypergraphs.Furthermore, an algorithm for computing independent sets of size asguaranteed by the lower bound is given. © 1999 John Wiley& Sons, Inc. J Graph Theory 30: 213221, 1999