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...
| Main Authors: | , , |
|---|---|
| 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 |
| id |
doaj-1b288c90d41d45379fc2afc3f19ceeb5 |
|---|---|
| record_format |
Article |
| spelling |
doaj-1b288c90d41d45379fc2afc3f19ceeb52020-11-25T00:22:42ZengCarleton UniversityJournal of Computational Geometry1920-180X2014-03-015110.20382/jocg.v5i1a346Which point sets admit a $k$-angulation?Michael S. Payne0Jens M. Schmidt1David R. Wood2The University of MelbourneTU IlmenauMonash UniversityFor \(k\ge 3\), 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.http://jocg.org/index.php/jocg/article/view/92 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Michael S. Payne Jens M. Schmidt David R. Wood |
| spellingShingle |
Michael S. Payne Jens M. Schmidt David R. Wood Which point sets admit a $k$-angulation? Journal of Computational Geometry |
| author_facet |
Michael S. Payne Jens M. Schmidt David R. Wood |
| author_sort |
Michael S. Payne |
| title |
Which point sets admit a $k$-angulation? |
| title_short |
Which point sets admit a $k$-angulation? |
| title_full |
Which point sets admit a $k$-angulation? |
| title_fullStr |
Which point sets admit a $k$-angulation? |
| title_full_unstemmed |
Which point sets admit a $k$-angulation? |
| title_sort |
which point sets admit a $k$-angulation? |
| publisher |
Carleton University |
| series |
Journal of Computational Geometry |
| issn |
1920-180X |
| publishDate |
2014-03-01 |
| description |
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. |
| url |
http://jocg.org/index.php/jocg/article/view/92 |
| work_keys_str_mv |
AT michaelspayne whichpointsetsadmitakangulation AT jensmschmidt whichpointsetsadmitakangulation AT davidrwood whichpointsetsadmitakangulation |
| _version_ |
1725358730144382976 |