On the complexity of graph coloring with additional local conditions
Abstract
Let $G = (V,E)$ be a finite simple graph. Recall that a proper coloring of $G$ is a mapping $\varphi: V\to\{1,\ldots,k\}$ such that every color class induces an independent set. Such a $\varphi$ is called a semimatching coloring if the union of any two consecutive color classes induces a matching. We show that the semimatching coloring problem is NPcomplete for any fixed $k\geqslant 3$, 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 DOI:
 10.48550/arXiv.1712.03150
 arXiv:
 arXiv:1712.03150
 Bibcode:
 2017arXiv171203150S
 Keywords:

 Mathematics  Combinatorics
 EPrint:
 4 pages