### Bay Area Discrete Math Day XII: The Coloring Torus of a...

Google TechTalksBay Area Discrete Math Day XIIApril 15, 2006Dave Bayer (Barnard College, Columbia University)ABSTRACTCircular colorability geometrizes the study of graph colorings. Using color values in R mod Z, one can reformulate "avoid edge differences close to zero" as " seek edge differences close to 1/2", then generalize to arbitrary edge difference goals. We define the coloring torus Xg of a graph G to be the space of all such coloring problems. X is made of the same stuff as the color values R mod Z: it is R mod L for a lattice L, so we can apply toric methods to its study. For planar graphs, the observed distances from 0 to torsion points of Xg form a pattern generalizing the four...

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