Schmidt, Jens M.Jens M.SchmidtValtr, PavelPavelValtr2020-10-212020-10-212015Computational Geometry: Theory and Applications (2015)http://hdl.handle.net/11420/7631Let 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 (0-, 1- or 2-connected) 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 that checks for 2-connected cubic plane graphs; the algorithm is constructive and runs in time O(n3). We also show which graph structure can be expected when there is a cubic plane graph on P; e. g., a cubic plane graph on P implies a connected cubic plane graph on P, and a 2-connected cubic plane graph on P implies a 2-connected cubic plane graph on P that contains the boundary cycle of P. We extend the above algorithm to check for arbitrary cubic plane graphs in time O(n3).en0925-7721201511133-Regular embeddingk-Connected cubic graphPlane graphs on pointsPolynomial time algorithmMathematikJournal Article10.1016/j.comgeo.2014.06.001Other