2025/02/17 by Shohei Satake, Satake, Shohei
Computer Science · Engineering · Mathematics · #05C20 #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Rings, Modules, and Algebras #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2502.12090
openalex publication_date 2025/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nearly-doubly-regular tournaments have played significant roles in extremal graph theory. In this note, we construct new cyclotomic nearly-doubly-regular tournaments and determine their spectrum by establishing a new connection between cyclotomic nearly-doubly-regular tournaments and almost difference sets from combinatorial design theory. Furthermore, under the celebrated Hardy-Littlewood conjecture F in analytic number theory, our results confirm the conjecture due to Sergey Savchenko (J. Graph Theory \bf 83 (2016), 44--77) on the existence of infinitely many nearly-doubly-regular tournaments with the canonical spectrum.