On the forbidden induced subgraph sandwich problem

Weconsider the sandwich problem, a generalization of the recognition problem introduced by Golumbic et al. (1995) [15], with respect to classes of graphs defined by excluding induced subgraphs. We prove that the sandwich problem corresponding to excluding a chordless cycle of fixed length k is NP-complete. We prove that the sandwich problem corresponding to excluding Kr \ e for fixed r is polynomial. We prove that the sandwich problem corresponding to 3PC(·, ·)-free graphs is NP-complete. These complexity results are related to the classification of a long-standing open problem: the sandwich problem corresponding to perfect graphs. © 2010 Elsevier B.V. All rights reserved.