Star-critical Ramsey numbers and regular Ramsey numbers for stars
Zhidan Luo

TL;DR
This paper investigates star-critical and regular Ramsey numbers for star graphs, providing exact formulas that disprove a previous conjecture and depend on the parity of the number of even parameters.
Contribution
It establishes explicit formulas for star-critical and regular Ramsey numbers for stars, disproving a conjecture and highlighting the role of parity in these calculations.
Findings
Exact formula for star-critical Ramsey numbers for stars with even parameters.
Exact formula for regular Ramsey numbers depending on the parity of the parameters.
Disproof of a conjecture by Budden and DeJonge (2022).
Abstract
Let be a graph, be a subgraph of , and let be the graph obtained from by removing a copy of . Let be the star on vertices. Let be an integer and and be graphs, and let denote that every coloring of yields a monochromatic copy of in color for some . Ramsey number is the minimum integer such that . Star-critical Ramsey number is the minimum integer such that where . Let be the regular Ramsey number for , which is the minimum integer such that if is an -regular graph on vertices,…
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 · Advanced Graph Theory Research
