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The dimension of a graph G is defined to be the minimum n such that G has a representation as a unit-distance graph in R. A problem posed by Paul Erdős asks for the minimum number of edges in a graph of dimension 4. In a recent article, R. F. House showed that the answer to Erdős’ question is 9. In this article, we give a shorter (and we feel more(More)
A cover (with triples) of λK n is an ordered pair (V, B) where V is an n-element set and B is a set of 3-element subsets of V called blocks such that each 2-element subset of V appears in at least λ blocks. Define The excess (sometimes called the padding) of a cover is defined to be E(B) − E(λK n), although it is often convenient to think of the excess as(More)
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