Forbidden subgraphs implying the MIN-algorithm gives a maximum independent set

Authors:
Jochen Harant;Zdenek Ryjácek;Ingo Schiermeyer
Affiliations:
Department of Mathematics, Technical University of Ilmenau, D-98684 Ilmenau, Germany;Department of Mathematics, University of West Bohemia, 306 14 Pilsen, Czech Republic;Department of Mathematics, Freiberg University of Mining and Technology, D-09596 Freiberg, Germany
Venue:
Discrete Mathematics
Year:
2002

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Abstract

The well-known greedy algorithm MIN for finding a maximal independent set in a graph G is based on recursively removing the closed neighborhood of a vertex which has (in the currently existing graph) minimum degree. We give a forbidden induced subgraph condition under which algorithm MIN always results in finding a maximum independent set of G, and hence yields the exact value of the independence number of G in polynomial time.