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graphs that can be embedded into the plane, i.e. that can be drawn without crossings between the lines representing edges.

2 votes

Generalizations of Planar Graphs

Resembling the "quasiplanar graphs" that Joe Malkevitch mentioned, you have the class of graphs with crossing number (in the plane) at most k for any $k \geq 0$. For $k = 0$ these are exactly the plan …
Harrison Brown's user avatar
5 votes

Generalizations of Planar Graphs

Ooh, this is another "off the top of my head" one, but another generalization of the family of planar graphs is matroid families closed under taking duals.
Harrison Brown's user avatar
9 votes

Generalizations of Planar Graphs

Some of the broadest generalizations generalize the family of planar graphs. Possibly the most important generalization along these lines is the notion of a minor-closed graph family, among which the …
Harrison Brown's user avatar