For k >= 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.Comment: 13 pages, 7 figure

Payne, Michael S.

Schmidt, Jens M.

Wood, David R.

English

arXiv

For k ≥ 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 2k2 points, the only obstructions are those that follow from Euler’s formula

Michael S. Payne

Jens M. Schmidt

David R. Wood

CiteSeerX

Which point sets admit a k-angulation?

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

Directory of Open Access Journals

Which point sets admit a $k$-angulation?

For k≥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 2k² points, the only obstructions are those that follow from Euler’s formula

Which point sets admit a k-angulation?

Abstract

Similar works

Full text

Available Versions

CiteSeerX

Directory of Open Access Journals

Digitale Bibliothek Thüringen

Journal of Computational Geometry (JoCG - Carleton University, Computational Geometry Lab)