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Winter 2002 A "nice" map colour theorem
K. S. Sarkaria
Illinois J. Math. 46(4): 1111-1123 (Winter 2002). DOI: 10.1215/ijm/1258138469


A closed orientable triangulated surface is "nice" if its vertices can be assigned 4 colours in such a way that all 4 colours are used in the closed star of each edge. The 4-colouring can be interpreted as a simplicial map from the surface to the 4-vertex 2-sphere. If the surface has genus $(n-1)^2$, then the degree of this map is at least $n^2$. Conversely we show that, if $n$ is not divisible by 2 and 3, then there are "nice" surfaces of genus $(n-1)^2$ for which the degree of the above map is exactly $n^2$. Complex analytically "nice" surfaces can be viewed as minimally triangulated meromorphic functions of a Riemann surface.


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K. S. Sarkaria. "A "nice" map colour theorem." Illinois J. Math. 46 (4) 1111 - 1123, Winter 2002.


Published: Winter 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1030.57037
MathSciNet: MR1988253
Digital Object Identifier: 10.1215/ijm/1258138469

Primary: 57Q15
Secondary: 05C10, 55M25

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign


Vol.46 • No. 4 • Winter 2002
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