2024/02/13 by Jacob Fox, Fox, Jacob, Zoe Himwich +5
Business, Management and Accounting · Decision Sciences · Economics, Econometrics and Finance · #Combinatorics (math.CO) #Consumer Market Behavior and Pricing #Economic theories and models #FOS: Mathematics #Game Theory and Applications
paper · pdf · doi:10.48550/arxiv.2402.08418
openalex publication_date 2024/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study variants of Sidorenko's conjecture in tournaments, where new phenomena arise that do not have clear analogues in the setting of undirected graphs. We first consider oriented graphs that are systematically under-represented in tournaments (called tournament anti-Sidorenko). We prove that such oriented graphs must be quite sparse; specifically, the maximum number of edges of a k-vertex oriented graph which is tournament anti-Sidorenko is (1+o(1))klog2 k. We also give several novel constructions of oriented graphs that are systematically over-represented in tournaments (tournament Sidorenko); as a representative example, we show that most ways to delete an edge from a transitive tournament yield a tournament Sidorenko oriented graph. As an illustration of our methods, we characterize which orientations of stars are tournament Sidorenko and which are tournament anti-Sidorenko.