# Rational approximation of analytic functions by Gonchar A. A. By Gonchar A. A.

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Additional info for Rational approximation of analytic functions

Example text

For completeness, just let me mention a related problem. A double blocking set is a collection B, with the property that every line intersects B in at least two points. Is it true that a double blocking set in PG(2, p), p prime, contains at least 3p points? Here the situation is even worse: It is only known (and a not too difficult exercise) for p = 2,3,4,5, 7. We now proceed to consider blocking sets of a special type. If B has size q + N then a line can contain at most N points of B. If such a line exists the blocking set is called of Redei type.

Proof Let G be a simple graph with average degree at least d. We first show that, as is well known, every such G contains a bipartite graph, whose minimum degree is at least d/4. To see this, observe that G has an induced subgraph with minimum degree at least d/2, since one can repeatedly delete vertices of degree smaller than d/2 from G, as long as there are such vertices; since this process increases the average degree, it must terminate in a nonempty subgraph G' with minimum degree at least d/2.

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