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• W2891511267 abstract "How long a monotone path can one always find in any edge-ordering of the complete graph $K_n$? This appealing question was first asked by Chvatal and Komlos in 1971, and has since attracted the attention of many researchers, inspiring a variety of related problems. The prevailing conjecture is that one can always find a monotone path of linear length, but until now the best known lower bound was $n^{2/3-o(1)}$. In this paper we almost close this gap, proving that any edge-ordering of the complete graph contains a monotone path of length $n^{1-o(1)}$." @default.
• W2891511267 created "2018-09-27" @default.
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• W2891511267 date "2018-09-05" @default.
• W2891511267 modified "2023-09-23" @default.
• W2891511267 title "Nearly-linear monotone paths in edge-ordered graphs." @default.
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