The graph sandwich problem for 1-join composition is NP-complete

  • Authors:

  • Celina M. H. de Figueiredo;Sulamita Klein;Kristina Vusković

  • Affiliations:

  • IM and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil;IM and COPPE, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970 Rio de Janeiro, RJ, Brazil;School of Computing, University of Leeds, Leeds LS2 9JT, UK

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2002

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Abstract

A graph is a 1-join composition if its vertex set can be partitioned into four nonempty sets AL, AR , SL and SR such that: every vertex of AL is adjacent to every vertex of AR; no vertex of SL is adjacent to vertex of AR∪SR; no vertex of SR is adjacent to a vertex of AL∪SL. The graph sandwich problem for 1-join composition is defined as follows: Given a vertex set V, a forced edge set E1, and a forbidden edge set E3, is there a graph G= (V,E) such that E1 ⊆ E and E ∩ E3 = φ, which is a 1-join composition graph? We prove that the graph sandwich problem for 1-join composition is NP-complete. This result stands in contrast to the case where SL = φ (SR = φ), namely, the graph sandwich problem for homogeneous set, which has a polynomial-time solution.