The Number of Seymour Vertices in Random Tournaments and Digraphs |
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| Authors: | Zachary Cohn Anant Godbole Elizabeth Wright Harkness Yiguang Zhang |
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| Affiliation: | 1.University of Chicago,Chicago,USA;2.East Tennessee State University,Johnson City,USA;3.Tulane University,New Orleans,USA;4.The Johns Hopkins University,Baltimore,USA |
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| Abstract: | ![]()
Seymour’s distance two conjecture states that in any digraph there exists a vertex (a “Seymour vertex”) that has at least as many neighbors at distance two as it does at distance one. We explore the validity of probabilistic statements along lines suggested by Seymour’s conjecture, proving that almost surely there are a “large” number of Seymour vertices in random tournaments and “even more” in general random digraphs. |
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