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Johannes Carmesin, A Whitney type theorem for surfaces: characterising graphs with locally planar embeddings
Wednesday, May 12, 2021 @ 5:00 PM - 6:00 PM KST
Given a graph, how do we construct a surface so that the graph embeds in that surface in an optimal way? Thomassen showed that for minimum genus as optimality criterion, this problem would be NP-hard. Instead of minimum genus, here we use local planarity — and provide a polynomial algorithm.
Our embedding method is based on Whitney’s trick to use matroids to construct embeddings in the plane. Consequently we obtain a characterisation of the graphs admitting locally planar embeddings in surfaces in terms of a certain matroid being co-graphic.