Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4763. (January 2016)

B. 4763. Let $\displaystyle G$ be a simple undirected graph of $\displaystyle n$ vertices. Prove that it is possible to assign infinite sets $\displaystyle \mathcal{H}_1,\mathcal{H}_2, \dots, \mathcal{H}_n$ of natural numbers to the graph such that the intersection of two sets is infinite if the corresponding vertices are joined by an edge, and empty if there is no edge joining the vertices.

Proposed by G. Mészáros, Budapest

(4 pont)

Deadline expired on February 10, 2016.

### Statistics:

 105 students sent a solution. 4 points: 99 students. 3 points: 3 students. 2 points: 2 students. 1 point: 1 student.

Problems in Mathematics of KöMaL, January 2016