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Graphs with few paths of prescribed length between any two vertices

Conlon, David (2019) Graphs with few paths of prescribed length between any two vertices. . (Unpublished)

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We use a variant of Bukh's random algebraic method to show that for every natural number k ≥ 2 there exists a natural number ℓ such that, for every n, there is a graph with n vertices and Ω_(k)(n^(1 + 1/k)) edges with at most ℓ paths of length k between any two vertices. A result of Faudree and Simonovits shows that the bound on the number of edges is tight up to the implied constant.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Conlon, David0000-0001-5899-1829
Additional Information:Research supported by a Royal Society University Research Fellowship. I would like to thank Boris Bukh, Gal Kronenberg, Rudi Mrazović and Lisa Sauermann for a number of valuable comments on an earlier draft of this paper. I would also like to thank the anonymous referee for their considered review.
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Record Number:CaltechAUTHORS:20190819-170853333
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98021
Deposited By: Melissa Ray
Deposited On:20 Aug 2019 19:54
Last Modified:03 Oct 2019 21:37

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