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)
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.