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# Cubic plane graphs on a given point set

Publikationstyp

Conference Paper

Publikationsdatum

2012-07

Sprache

English

Author

TORE-URI

Start Page

201

End Page

208

Citation

SoCG '12: Proceedings of the twenty-eighth annual symposium on Computational geometry pp 201–208

Contribution to Conference

Publisher DOI

Scopus ID

Let P be a set of n ≥ 4 points in the plane that is in general position and such that n is even. We investigate the problem whether there is a cubic plane straight-line graph on P. No polynomial-time algorithm is known for this problem. Based on a reduction to the existence of certain diagonals of the boundary cycle of the convex hull of P, we give the first polynomial-time algorithm; the algorithm is constructive and runs in time O(n 3). We also show which graph structure can be expected when there is a cubic plane graph on P; e. g., if P admits a 2-connected cubic plane graph, we show that P admits also a 2-connected cubic plane graph that contains the boundary cycle of P. The algorithm extends to checking P on admitting a 2-connected cubic plane graph.