Problem A. 535. (April 2011)
A. 535. There is given a simple graph G with vertices v_{1},...,v_{n}. H_{1},...,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.
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