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Results tagged with planar-graphs
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user 1532
graphs that can be embedded into the plane, i.e. that can be drawn without crossings between the lines representing edges.
5
votes
Generalizations of Planar Graphs
Here is another generalization of planar graphs.
Start with a $d$-dimensional polytope $P$ with $n$ vertices. For every $2$-dimensional face $F$ triangulate $F$ by non crossing diagonals. So if $F$ h …
- 24.7k
9
votes
Generalizations of Planar Graphs
One interesting generalization is to "small classes of graphs." A class of graphs is small if the number of isomorphism classes of such graphs with n vertices is (only) exp (O(n)). Forests, planar gra …
- 32.1k
4
votes
Generalizations of Planar Graphs
Jarik Nesetril and Patrice Ossona de Mendez developed the notion of "nowhere dense graphs" which extends the class of planar graphs. The class of nowhere dense graphs include all graphs with a forbid …
- 24.7k
5
votes
Generalizations of Planar Graphs
Graphs which are stress-free for a generic embedding into space is an interesting class of graphs that includes all planar graphs.
One thing to notice is that edges of maximal planar graphs with n ve …
- 24.7k
2
votes
Generalizations of Planar Graphs
There are two interesting classes of directed planar graphs (where the undirected graph is 3-connected). One class consist of planar directed graphs with an acyclic unique sink property: those are acy …
- 24.7k