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arXiv · 1712.03150

On the complexity of graph coloring with additional local conditions

Yaroslav Shitov
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Abstract

Let $G = (V,E)$ be a finite simple graph. Recall that a proper coloring of $G$ is a mapping $φ: V\to\{1,\ldots,k\}$ such that every color class induces an independent set. Such a $φ$ 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 $k\geqslant 3$, 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.

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Yaroslav Shitov. 2017-12-08. On the complexity of graph coloring with additional local conditions. https://arxiv.org/abs/1712.03150

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