Problem A. 535. (April 2011)

A. 535. There is given a simple graph G with vertices v₁,...,v_n. H₁,...,H_n are sets of nonnegative integers such that for every i=1,2,...,n, the cardinality of H_i is at most half of the degree of v_i. Prove that G contains a subgraph G' with the same vertices such that the degree of v_i in G' is not an element of H_i for any i.

(Proposed by: László Miklós Lovász, Budapest)

(5 pont)

Deadline expired on May 10, 2011.

Statistics:

5 students sent a solution.
5 points:	Backhausz Tibor, Frankl Nóra, Nagy 235 János, Nagy 648 Donát.
2 points:	1 student.

Problems in Mathematics of KöMaL, April 2011