Mathematical and Physical Journal
for High Schools
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Problem A. 535. (April 2011)

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

(Proposed by: László Miklós Lovász, Budapest)

(5 pont)

Deadline expired on May 10, 2011.


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