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Date added: 13.3.2015

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In this paper we examine two problems. First, given n > 1, find a function f : NN where m = f(n) is the smallest natural number such that Km is intrinsically n-linked. The second is the analogous question for complete bipartite graphs: find theMoreIn this paper we examine two problems. First, given n > 1, find a function f : N→N where m = f(n) is the smallest natural number such that Km is intrinsically n-linked. The second is the analogous question for complete bipartite graphs: find the smallest natural numbers r, and s such that Kr,s is intrinsically n-linked. We prove, for n > 1, that every embedding of K&fll0-72n&flr0- in R3 contains a non-splittable link of n components. We also prove an asymptotic result, that there exists a function f( n) such that limn→infinity fnn = 3 and, for every n, Kf( n) is intrinsically n-linked. Next, we prove that every embedding of K2 n+1,2n+1 in R3 contains a non-splittable link of n components. Further, given an embedding of K2n +1,2n+1 in R3 , every edge of K2n +1,2n+1 is contained in a non-splittable n-component link in K2n +1,2n+1. Intrinsically n-linked spatial graphs. by Danielle Summer ODonnol