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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.

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"Constrained" Moser's Trick

I wish to know if there is a sort of "constrained Moser Trick". Suppose we have a planar grap $G \subseteq \mathbb{R}^2$, with $(0,0)$ as a vertex. Suppose to have some volume form $\omega = g_\ast(dx …
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Diffeomorphism of graph with conditions on volume from

I have the following situation: I have a graph $G$ embedded into $\mathbb{R}^2$, with $(0,0)$ a vertex, and I have a diffeomorphism $g$ of the plane. Let's call $G' = g(G)$ the new graph. I suppose th …
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