Between coloring and list-coloring: μ-coloring … Between coloring and list-coloring: μ-coloring …

A new variation of the coloring problem, mu-coloring, is defined in this paper. A coloring of a
graph G=(V, E) is a function f: V-> N such that f (v) is different from f (w) if v is adjacent to w.
Given a graph G=(V, E) and a function mu: V-> N, G is mu-colorable if it admits a coloring f
with f (v)<= mu (v) for each v in V. It is proved that mu-coloring lies between coloring and list-
coloring, in the sense of generalization of problems and computational complexity. Besides,
the notion of perfection is extended to mu-coloring, giving rise to a new characterization of …