Using Edge Exchanges to Prove the Erdős-jacobson-lehel Conjecture

We consider a problem in extremal graph theory as introduced by Erdős, Jacobson and Lehel in [3]. That is, given an n-term graphic degree sequence, for n sufficiently large, we prove that the minimum degree sum necessary to guarantee a realization containing a t-clique, t ≥ 2, is (t − 2)(2n − t + 1) + 2. The proof involves the notion of an edge exchange, which is well-known but has not been used in previous approaches to this problem. It is our hope that the proof will demonstrate the utility of this technique and inspire new approaches to similar problems.