2017/10/30 by Hannah Guggiari, Guggiari, Hannah · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO
paper · pdf · doi:10.48550/arxiv.1710.10900
arxiv created 2017/10/30 · openalex publication_date 2017/10/30 · arxiv updated 2017/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Kℕ be the complete symmetric digraph on the positive integers. Answering a question of DeBiasio and McKenney, we construct a 2-colouring of the edges of Kℕ in which every monochromatic path has density 0. On the other hand, we show that, in every colouring that does not have a directed path with r edges in the first colour, there is directed path in the second colour with density at least \frac1r.