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On the complexity of graph coloring with additional local conditions
Let be a finite simple graph. Recall that a proper coloring of
is a mapping such that every color class
induces an independent set. Such a is called a semi-matching coloring
if the union of any two consecutive color classes induces a matching. We show
that the semi-matching coloring problem is NP-complete for any fixed
, and we get the same result for another version of this problem
in which any triangle of G is required to have vertices whose colors differ at
least by three.Comment: 4 page