Forbidden induced subgraph characterization of cograph contractions

  • Authors:

  • Igor Ed. Zverovich;Inessa I. Zverovich

  • Affiliations:

  • RUTCOR-Rutgers Center for Operations Research, Rutgers, The State University of New Jersey, 640 Bartholomew Road, Piscataway, New Jersey 08854-8003;RUTCOR-Rutgers Center for Operations Research, Rutgers, The State University of New Jersey, 640 Bartholomew Road, Piscataway, New Jersey 08854-8003

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2004

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Abstract

Let S1,S2,…,St be pairwisedisjoint non-empty stable sets in a graph H. The graphH* is obtained from H by: (i) replacingeach Si by a new vertex qi;(ii) joining each qi and qj, 1≤ i # j ≤ t, and; (iii) joiningqi to all vertices in H(S1 ∪ S2 ∪··· ∪ St) which wereadjacent to some vertex of Si. A cographis a P4-free graph. A graph G is called acograph contraction if there exist a cograph H andpairwise disjoint non-empty stable sets in H for whichG ≃ H*. Solving a problemproposed by Le [2], we give a finite forbidden induced subgraphcharacterization of cograph contractions. © 2004 WileyPeriodicals, Inc. J Graph Theory 46: 217226, 2004