Classic 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 in the most general setting and "mix" it with the old approach.
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.
Only God knows what is coming next in this direction...
WORM Coloring of Graphs: a brilliant example showing that basic concepts of
mixed hypergraph coloring provide a wealthy source of infinitely many
beautiful problems in graph theory