Monotone Paths in Dense Edge-Ordered Graphs
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چکیده
The altitude of a graphG, denoted f(G), is the largest integer k such that under each ordering of E(G), there exists a path of length k which traverses edges in increasing order. In 1971, Chvátal and Komlós asked for f(Kn), where Kn is the complete graph on n vertices. In 1973, Graham and Kleitman proved that f(Kn) ≥ √ n− 3/4− 1/2 and in 1984, Calderbank, Chung, and Sturtevant proved that f(Kn) ≤ ( 12 +o(1))n. We show that f(Kn) ≥ ( 1 20−o(1))(n/ lg n) .
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تاریخ انتشار 2015