# Questions tagged [planar-graphs]

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20 questions
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### “Locally Nonplanar” graph

A 2-connected $3$-connected graph $G$ is "Almost Planar" Locally Nonplanar if it has a a $2$-connected spanning subgraph $H$ and an embedding in the plane such that $H$ is planar in this embedding and ...
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### When is an ordering of edges in a graph a planar embedding?

Is there a criterion which decides whether a given rotation system for a graph determines a planar embedding? That is, a lemma of the form: A graph G = (V, E) is planar if and only if there exists ...
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### Is there easy proof for triangle-free two-coloring of planar graphs?

By merging two-two color classes, the Four Color Theorem implies that every planar graph can be two-colored such that each color class induces a triangle-free graph. Is there a simpler proof for this ...
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### In how many ways can a given planar graph be mapped into the plane?

I feel sure that this question must have been addressed in the literature, but I can't seem to find it - I may be looking in the wrong place. A graph is planar if it can be drawn on the plane such ...