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...

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Bibliographic Details
Main Authors:	Michael S. Payne, Jens M. Schmidt, David R. Wood
Format:	Article
Language:	English
Published:	Carleton University 2014-03-01
Series:	Journal of Computational Geometry
Online Access:	http://jocg.org/index.php/jocg/article/view/92

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Summary:	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.
ISSN:	1920-180X

Summary:	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.
ISSN:	1920-180X

Which point sets admit a $k$-angulation?

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