The graph sandwich problem for property ⊆ is defined as follows: Given two graphs G1 = (V, E1) and G2 = (V, E2) such that E1 ⊆ E2, is there a graph G = (V, E) such that E1 ⊆ E ⊆ E2 which satisfies property ⊆? Such problems generalize recognition problems and arise in various applications. Concentrating mainly on properties characterizing subfamilies of perfect graphs, we give polynomial algorithms for several properties and prove the NP-completeness of others. We describe polynomial time algorithms for threshold graphs, split graphs, and cographs. For the sandwich problem for threshold graphs, the only case in which a previous algorithm existed, we obtain a faster algorithm. NP-completeness proofs are given for comparability graphs, permutation graphs, and several other families. For Eulerian graphs; one Version of the problem is polynomial and another is NP-complete.
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics