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A Criterion for Planar Graphs

https://www.youtube.com/watch?v=be8AKUAAuZs It is difficult to know in general when a graph has a planar embedding without actually seeing a planar embedding. However, we can derive a necessary criterion for planarity using Euler’s characteristic formula, depending only on the number of vertices and edges of the graph (making it independent of any particular planar embedding). By

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