Which point sets admit a $k$-angulation?

Michael S. Payne, Jens M. Schmidt, David R. Wood


For \(k\ge 3\), a \(k\)-angulation is a 2-connected plane graph in which every internal face is a \(k\)-gon. We say that a point set \(P\) admits a plane graph \(G\) if there is a straight-line drawing of \(G\) that maps \(V(G)\) onto \(P\) and has the same facial cycles and outer face as \(G\). We investigate the conditions under which a point set \(P\) admits a \(k\)-angulation and find that, for sets containing at least \(2k^2\) points, the only obstructions are those that follow from Euler's formula.

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DOI: http://dx.doi.org/10.20382/jocg.v5i1a3

ISSN: 1920-180X