Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# 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