Schmidt, Jens M.Jens M.SchmidtValtr, PavelPavelValtr2020-10-212020-10-212012-0728th Annual Symposuim on Computational Geometry (SCG 2012)http://hdl.handle.net/11420/7632Let 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.enCubic graphsPlanar embeddingPoint setTechnology::600: TechnologyConference Paper10.1145/2261250.2261281Conference Paper