2-subcoloring is NP-complete for planar comparability graphs

2-subcoloring is NP-complete for planar comparability graphs

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 P3. 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 ...

k-L(2, 1)-labelling for planar graphs is NP-complete for k>=4

A mapping from the vertex set of a graph G = (V,E) into an interval of integers {0, . . . , k} is an L(2, 1)-labelling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbour are mapped onto distinct integers. It is known that for any fixed k ≥ 4, deciding the existence of such a labelling is an NP-complete p...

k-L(2, 1)-Labelling for Planar Graphs is NP-Complete

A mapping from the vertex set of a graph G = (V,E) into an interval of integers {0, . . . , k} is an L(2, 1)-labelling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common neighbour are mapped onto distinct integers. It is known that for any fixed k ≥ 4, deciding the existence of such a labelling is an NP-complete p...

Uniform Planar Embedding Is Np - Complete

Planar Metric Dimension is NP-complete

We show that Metric Dimension on planar graphs is NP-complete.