Journal of Algorithms
The homogeneous set sandwich problem
Information Processing Letters
An efficient algorithm for solving the homogeneous set sandwich problem
Information Processing Letters
The pair completion algorithm for the homogeneous set sandwich problem
Information Processing Letters
The Pair Completion algorithm for the Homogeneous Set Sandwich Problem
Information Processing Letters
Complexity issues for the sandwich homogeneous set problem
Discrete Applied Mathematics
| Hi-index | 0.89 |
A module is a set of vertices H of a graph G = (V,E) such that each vertex of V \ H is either adjacent to all vertices of H or to none of them. A homogeneous set is a nontrivial module. A graph Gs = (V, Es) is a sandwich for a pair of graphs Gt = (V,Et) and G = (V,E) if Et ⊆ Es ⊆ E. In a recent paper, Tang et al. [Inform. Process. Lett. 77 (2001) 17-22] described an O(Δn2) algorithm for testing the existence of a homogeneous set in sandwich graphs of Gt = (V, Et) and G = (V,E) and then extended it to an enumerative algorithm computing all these possible homogeneous sets. In this paper, we invalidate this latter algorithm by proving there are possibly exponentially many such sets, even if we restrict our attention to strong modules. We then give a correct characterization of a homogeneous set of a sandwich graph.