Math @ Duke

Publications [#235793] of Robert Calderbank
Papers Published
 Calderbank, AR; Chung, FRK; Sturtevant, DG, Increasing sequences with nonzero block sums and increasing paths in edgeordered graphs,
Discrete Mathematics, vol. 50 no. C
(1984),
pp. 1528, ISSN 0012365X
(last updated on 2017/12/15)
Abstract: Consider the maximum length f(k) of a (lexicographically) increasing sequence of vectors in GF(2)k with the property that the sum of the vectors in any consecutive subsequence is nonzero modulo 2. We prove that 23 48 · 2k ≤ f(k) ≤ ( 1 2 + o(1))2k. A related problem is the following. Suppose the edges of the complete graph Kn are labelled by the numbers 1,2,..., (2n). What is the minimum α(n), over all edge labellings, of the maximum length of a simple path with increasing edge labels? We prove that α(n) ≤ ( 1 2 + o(1))n. © 1984.


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