Local chromatic number of quadrangulation of surfaces
Microsoft
Local chromatic number of quadrangulation of surfaces
A quadrangulation of a surface is a graph embedded in the surface such that every face is a quadrangle. Clearly, such graphs in the plane are bipartite, but some quadrangulations of the torus are 3-chromatic. A surprising result of Youngs states that quadrangulations of the projective plane are either bipartite or 4-chromatic. A generalization ...
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