Case 0 of the Map Color Theorem
Tuesday,
February 5, 2019
10:10 AM - 11:10 AM
Department of Computer Science, 500 W. 120th St., New York, New York 10027
Room/Area: Conference Room 453
Room/Area: Conference Room 453
Abstract:
The Map Color Theorem is a fundamental result in topological graph theory that gives a formula for the maximum number of colors needed to color a map of countries on a given surface. The most complicated part of the proof is so-called "Case 0," which concerns computing the minimum-genus surfaces that the complete graphs on 12n vertices embed in. Previous solutions of this case were complicated, where the simplest proof due to Terry et al. relies on advanced tools from abstract algebra. The purpose of this talk is to highlight a recent result that is significantly easier than all aforementioned constructions. We present a simple family of symmetric embeddings modifiable into triangular embeddings of the aforementioned complete graphs. No knowledge of graph theory or topology will be assumed.
The Map Color Theorem is a fundamental result in topological graph theory that gives a formula for the maximum number of colors needed to color a map of countries on a given surface. The most complicated part of the proof is so-called "Case 0," which concerns computing the minimum-genus surfaces that the complete graphs on 12n vertices embed in. Previous solutions of this case were complicated, where the simplest proof due to Terry et al. relies on advanced tools from abstract algebra. The purpose of this talk is to highlight a recent result that is significantly easier than all aforementioned constructions. We present a simple family of symmetric embeddings modifiable into triangular embeddings of the aforementioned complete graphs. No knowledge of graph theory or topology will be assumed.
Bio:
Timothy Sun is a 6th year PhD candidate at Columbia University advised by Prof. Rocco Servedio and Prof. Xi Chen. His recent research interests center on graph theory and property testing. He was also at Columbia as an undergraduate in SEAS, working with Prof. Jonathan L. Gross in topological graph theory.
Timothy Sun is a 6th year PhD candidate at Columbia University advised by Prof. Rocco Servedio and Prof. Xi Chen. His recent research interests center on graph theory and property testing. He was also at Columbia as an undergraduate in SEAS, working with Prof. Jonathan L. Gross in topological graph theory.
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