On Stubborn Graph Sandwich Problems

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 G
¹
= (V, E
¹
), G
²
= (V,E
²
) such that if E
¹
sube E
²
, 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 E
¹
sube E sube E
²
. In this paper, we prove that the LIST STUBBORN GRAPH SANDWICH PROBLEM is N/P-complete.