And Increasing Paths in Ktm~e-ordered Graphs
نویسنده
چکیده
Consider the maximum length [(k) of a flexicographieally) 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 ~ . 2 k ~<f(k)~<(~+o(1))2 k. A related problem is the following. Suppose the edges of the complete graph K , are labelled by the numbers 1,2 . . . . . (~.). What is the minimum a(n), over all edge labellings, of the maximum length of a simple path with increasing edge labels? We prove that a (n)~< (21 + o(1))n.
منابع مشابه
Characterization of signed paths and cycles admitting minus dominating function
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