Problem A. 683. (December 2016)

A. 683. Let \(\displaystyle K=(V,E)\) be a finite, simple, complete graph. Let \(\displaystyle \phi\colon E\to\mathbb{R}^2\) be a map from the edge set to the plane, such that the preimage of any point in the range defines a connected graph on the entire vertex set \(\displaystyle V\), and the points assigned to the edges of any triangle are collinear. Show that the range of \(\displaystyle \phi\) is contained in a line.

(Based on a problem of the Miklós Schweitzer competition)

(5 pont)

Deadline expired on January 10, 2017.

Statistics:

6 students sent a solution.
5 points:	Baran Zsuzsanna, Bukva Balázs, Williams Kada.
4 points:	Matolcsi Dávid.
2 points:	1 student.
1 point:	1 student.

Problems in Mathematics of KöMaL, December 2016