Problem B. 4733. (October 2015)

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

(3 pont)

Deadline expired on November 10, 2015.

Statistics:

204 students sent a solution.
3 points:	170 students.
2 points:	13 students.
1 point:	7 students.
0 point:	12 students.
Unfair, not evaluated:	2 solutionss.

Problems in Mathematics of KöMaL, October 2015