ARTICLE
TITLE

Turán Numbers for 3-Uniform Linear Paths of Length 3

SUMMARY

In this paper we confirm a special, remaining case of a conjecture of Füredi, Jiang, and Seiver, and determine an exact formula for the Turán number ex3(n;P33)\mathrm{ex}_3(n; P_3^3) of the 3-uniform linear path P33P^3_3 of length 3, valid for all nn. It coincides with the analogous formula for the 3-uniform triangle C33C^3_3, obtained earlier by Frankl and Füredi for n=75n\ge 75 and Csákány and Kahn for all nn. In view of this coincidence, we also determine a `conditional' Turán number, defined as the maximum number of edges in a P33P^3_3-free 3-uniform hypergraph on nn vertices which is not C33C^3_3-free.

PAGES
pp. P2.30

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