k-L(2, 1)-Labelling for Planar Graphs is NP-Complete
نویسندگان
چکیده
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 problem while it is polynomial for k ≤ 3. For even k ≥ 8, it remains NP-complete when restricted to planar graphs. In this paper, we show that it remains NP-complete for any k ≥ 4 by reduction from Planar Cubic Two-Colourable Perfect Matching. Schaefer stated without proof that Planar Cubic Two-Colourable Perfect Matching is NP-complete. In this paper we give a proof of this.
منابع مشابه
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...
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