Problem A. 777. (May 2020)

A. 777. Finite graph \(\displaystyle G(V,E)\) on \(\displaystyle n\) points is drawn in the plane. For an edge \(\displaystyle e\) of the graph let \(\displaystyle x(e)\) denote the number of edges that cross over edge \(\displaystyle e\). Prove that

\(\displaystyle \sum\limits_{e\in E} \frac{1}{x(e)+1}\le 3n-6. \)

Submitted by Dömötör Pálvölgyi, Budapest

(7 pont)

Deadline expired on June 10, 2020.

Statistics:

4 students sent a solution.
7 points:	Bán-Szabó Áron, Beke Csongor, Matin Yousefi, Weisz Máté.

Problems in Mathematics of KöMaL, May 2020