Problem A. 747. (March 2019)

A. 747. In a simple graph on \(\displaystyle n\) vertices, every set of \(\displaystyle k\) vertices has an odd number of common neighbours. Prove that \(\displaystyle n+k\) must be odd.

Proposed by: András Imolay, Dávid Matolcsi, Ádám Schweitzer and Kristóf Szabó, Budapest

(7 pont)

Deadline expired on April 10, 2019.

Statistics:

3 students sent a solution.
7 points:	Schrettner Jakab, Weisz Máté.
2 points:	1 student.

Problems in Mathematics of KöMaL, March 2019