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