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Some Graph-Colouring Theorems With Applications To Generalized Connection Networks, David G. Kirkpatrick, Maria M. Klawe, Nicholas Pippenger

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With the aid of a new graph-colouring theorem, we give a simple explicit construction for generalized n-connectors with 2k - 1 stages and O( n^{1 + 1 / k} (log n )^{( k - 1)/ 2} ) edges. This is asymptotically the best explicit construction known for generalized connectors.