Corpus ID: 15800265

Nodally 3-connected planar graphs and convex combination mappings

@inproceedings{Dunlaing2007Nodally3P,
  title={Nodally 3-connected planar graphs and convex combination mappings},
  author={Colm O. Dunlaing},
  year={2007}
}
A barycentric mapping of a planar graph is a plane embedding in which every internal vertex is the average of its neighbours. A celebrated result of Tutte’s [16] is that if a planar graph is nodally 3-connected then such a mapping is an embedding. Floater generalised this result to convex combination mappings in which every internal vertex is a proper weighted average of its neighbours. He also generalised the result to all triangulated planar graphs. This has applications in numerical analysis… Expand
2 Citations
A Simple Criterion for Nodal 3-connectivity in Planar Graphs
  • 1
  • PDF

References

SHOWING 1-10 OF 21 REFERENCES
One-to-one piecewise linear mappings over triangulations
  • M. Floater
  • Computer Science, Mathematics
  • Math. Comput.
  • 2003
  • 121
  • Highly Influential
  • PDF
How to draw a planar graph on a grid
  • 697
Parametrization and smooth approximation of surface triangulations
  • M. Floater
  • Mathematics, Computer Science
  • Comput. Aided Geom. Des.
  • 1997
  • 799
  • Highly Influential
  • PDF
An Introduction to Convex Polytopes
  • 592
  • Highly Influential
  • PDF
Convex Combination Maps
  • 15
  • PDF
Classical topology and combinatorial group theory
  • 535
Lectures in algebraic topology
  • 302
  • PDF
The Dissection of Rectangles Into Squares
  • 315
  • Highly Influential
Algorithms in Combinatorial Geometry
  • H. Edelsbrunner
  • Mathematics, Computer Science
  • EATCS Monographs in Theoretical Computer Science
  • 1987
  • 2,327
Algorithms for drawing planar graphs
  • 100
  • Highly Influential
...
1
2
3
...