B. 4733. Every edge of a simple connected graph of \(\displaystyle n\ge 2\) vertices is labelled with either a 1 or with a 2. Then each vertex is assigned with the product of the numbers on the edges product of the numbers on the related edges on it. Show that there will be a pair of two vertices assigned with the same number.
Proposed by A. Hujdurović, Koper
Deadline expired on 10 November 2015.