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3 votes
1 answer
158 views

Sharp upper bound of the number of edges for graphs of thickness two

A graph $G=(V,E)$ has thickness $2$ if $E$ can be written as a disjoint union $E=E_1\cup E_2$ so that $G_1:=(V,E_1),G_2:=(V,E_2)$ are planar graphs. For instance, $K_5$ has thickness $2$. It is known ...
Lorenzo Pompili's user avatar
4 votes
1 answer
451 views

Implementation of Koebe–Andreev–Thurston circle packing?

The circle packing theorem (Koebe–Andreev–Thurston theorem) claims for a planar graph, we can pack disjoint circles, such that: the circles correspond to vertices and the disks are tangent if the ...
Jake B.'s user avatar
  • 1,465
4 votes
0 answers
281 views

Reference for results about planar graphs

A colleague and I are writing a paper in which we need to make use of some basic facts about planar graphs. I would strongly prefer to simply give references for the results if possible, because the ...
David Roberson's user avatar