TOT 196 1988 Autumn Train S3 natural at each vertex of polyhedron
Source:
March 7, 2021
polyhedroncombinatoricscombinatorial geometry
Problem Statement
Prove that for each vertex of a polyhedron it is possible to attach a natural number so that for each pair of vertices with a common edge, the attached numbers are not relatively prime (i.e. they have common divisors), and with each pair of vertices without a common edge the attached numbers are relatively prime. (Note: there are infinitely many prime numbers.)