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arXiv · 1702.01283

2-subcoloring is NP-complete for planar comparability graphs

Pascal Ochem
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Abstract

A $k$-subcoloring of a graph is a partition of the vertex set into at most $k$ cluster graphs, that is, graphs with no induced $P_3$. 2-subcoloring is known to be NP-complete for comparability graphs and three subclasses of planar graphs, namely triangle-free planar graphs with maximum degree 4, planar perfect graphs with maximum degree 4, and planar graphs with girth 5. We show that 2-subcoloring is also NP-complete for planar comparability graphs with maximum degree 4.

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Pascal Ochem. 2017-02-04. 2-subcoloring is NP-complete for planar comparability graphs. https://arxiv.org/abs/1702.01283

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