Classical graph coloring theory is the theory for finding the minimum number of colors. The basic idea of mixed hypergraphs is to introduce the problem of finding the maximum number of colors.
The main conclusion is that in trying to establish a formal symmetry between the two types of opposite constraints we find a deep asymmetry between the problems on minimum and problems on maximum number of colors. This asymmetry pervades the theory, methods, algorithms and applications of mixed hypergraph coloring.
