The Number of Seymour Vertices in Random Tournaments and Digraphs
Document Type
Article
Publication Date
9-1-2016
Description
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.
Citation Information
Cohn, Zachary; Godbole, Anant; Harkness, Elizabeth Wright; and Zhang, Yiguang. 2016. The Number of Seymour Vertices in Random Tournaments and Digraphs. Graphs and Combinatorics. Vol.32(5). 1805-1816. https://doi.org/10.1007/s00373-015-1672-9 ISSN: 0911-0119