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
Deadline expired on April 10, 2019.
3 students sent a solution. 7 points: Schrettner Jakab, Weisz Máté. 2 points: 1 student.