Asymptotics of Ramsey numbers of double stars
Sergey Norin, Yue Ru Sun, Yi Zhao

TL;DR
This paper investigates the Ramsey numbers of double star graphs, extending previous results with computational methods and identifying ranges where the conjecture holds or fails, also addressing a question from 1982.
Contribution
The authors extend known bounds on Ramsey numbers of double stars using flag algebra computations and identify specific parameter ranges where the conjecture does not hold.
Findings
Confirmed the conjecture for certain parameter ranges using computational methods.
Disproved the conjecture for other parameter ranges, providing counterexamples.
Answered a long-standing question from 1982 with new examples.
Abstract
A double star is the graph obtained by joining the center of a star with leaves to a center of a star with leaves by an edge. Let denote the Ramsey number of the double star . In 1979 Grossman, Harary and Klawe have shown that for and . They conjectured that equality holds for all . Using a flag algebra computation, we extend their result showing that for . On the other hand, we show that the conjecture fails for . Our examples additionally give a negative answer to a question of Erd\H{o}s, Faudree, Rousseau and Schelp from 1982.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Analytic Number Theory Research
