2016/02/04 by Dániel Korándi, Benny Sudakov, Korándi, Dániel +1
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1602.01697
openalex publication_date 2016/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A 3-tournament is a complete 3-uniform hypergraph where each edge has a special vertex designated as its tail. A vertex set X dominates T if every vertex not in X is contained in an edge whose tail is in X. The domination number of T is the minimum size of such an X. Generalizing well-known results about usual (graph) tournaments, Gyárfás conjectured that there are 3-tournaments with arbitrarily large domination number, and that this is not the case if any four vertices induce two triples with the same tail. In this short note we solve both problems, proving the first conjecture and refuting the second.