The chromatic spectrum of mixed hypergraphs

A mixed hypergraph is a triple H = (X, C, D), where X is the vertex set, and each of C, D is a list of subsets of X. A strict k-coloring of H is a surjection c : X --> {1,...,k} such that each member of C has two vertices. assigned a common value and each member of D has two vertices assigned distinct values. The feasible set of H is {k:H has a strict k-coloring}. Among other results,we prove that a finite set of positive integers is the feasible set of some mixed hypergraph if and only if it omits the number 1 or is an interval starting with 1. For the set {s,t} with 2 less than or equal to s less than or equal to t - 2, the smallest realization has 2t - s vertices. When every member of C boolean OR D is a single interval in an underlying linear order on the vertices, the feasible set is also a single interval of integers.