k-Independence and the k-residue of a graph

  • Authors:

  • Frank Jelen

  • Affiliations:

  • Lehrstuhl II für Mathematik, RWTH Aachen, Germany

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

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Abstract

Favaron, Mahéo, and Saclé proved that the residueof a simple graph G is a lower bound on its independencenumber ε (G). For k ε ℕ;, avertex set X in a graph is called k-independent, ifthe subgraph induced by X has maximum degree less thank. We prove that a generalization of the residue, thek-residue of a graph, yields a lower bound on thek-independence number. The new bound strengthens a bound ofCaro and Tuza and improves all known bounds for some graphs. ©1999 John Wiley & Sons, Inc. J Graph Theory 32: 241249,1999