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- W4362656057 abstract "While planar graphs are flat from a topological viewpoint, we observe that they are not from a geometric one. We prove that every planar graph can be embedded into a surface consisting of spheres, glued together in a tree-like fashion. As a technical ingredient we prove a statement implying an inverse of the Jordan curve theorem. This statement helps to identify cycles in the planar graph, corresponding to circles of latitude on the spheres. The tree-like embedding then allows for an inductive construction of a four-coloring of the planar graph. Hence, this yields a simple proof of the Four-Color Theorem." @default.
- W4362656057 created "2023-04-07" @default.
- W4362656057 creator A5088104983 @default.
- W4362656057 date "2023-04-02" @default.
- W4362656057 modified "2023-10-18" @default.
- W4362656057 title "A geometric view on planar graphs and its application to coloring" @default.
- W4362656057 doi "https://doi.org/10.48550/arxiv.2304.01925" @default.
- W4362656057 hasPublicationYear "2023" @default.
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