colouring of edges of a convex polyhedron
Source: All-Russian 2007
May 4, 2007
combinatorics unsolvedcombinatorics
Problem Statement
Given a convex polyhedron . Its vertex has degree , other vertices have degree . A colouring of edges of is called nice, if for any vertex except all three edges from it have different colours. It appears that the number of nice colourings is not divisible by . Prove that there is a nice colouring, in which some three consecutive edges from are coloured the same way.
D. Karpov