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dc.contributor.authorEggemann, N-
dc.contributor.authorHavet, F-
dc.contributor.authorNoble, S D-
dc.description.abstractA 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.en
dc.subjectfrequency assignment problemen
dc.subjectgraph labellingen
dc.subjectplanar graphen
dc.titlek-L(2, 1)-labelling for planar graphs is NP-complete for k>=4en
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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