Well-spread sequences and edge-labellings with constant Hamilton-weight

Abstract

A sequence (ai) of integers is well-spread if the sums a i + aj, for i < j, are all different. For a fixed positive integer r, let Wr(N) denote the maximum integer n for which there exists a well-spread sequence 0 ≤ a1 < ⋯ < an ≤ N with ai ≡ aj (mod r) for all i, j. We give a new proof that Wr(N) < Λ(n) < 2n2 + O(n61/40). © 2004 Discrete Mathematics and Theoretical Computer Science (DMTCS).