On Stubborn Graph Sandwich Problems

Abstract

The stubborn partition is a partition of the vertex set of a graph G into at most four parts A, B, C, D, with the following constraints: the internal constraints are part A and part B are required to be independent sets, and part D is required to be a clique; the only external constraint is that each vertex of part A is nonadjacent to every vertex of part C. This problem is generalized to the list sandwich version: given two graphs G¹ = (V, E¹), G² = (V,E²) such that if E¹ sube E², and for each vertex a list of parts in which the vertex is allowed to be placed, we look for a stubborn sandwich graph G = (V, E) such that E¹ sube E sube E². In this paper, we prove that the LIST STUBBORN GRAPH SANDWICH PROBLEM is N/P-complete.