Gallai Ramsey number for double stars
Gyula O.H. Katona, Colton Magnant, Yaping Mao, Zhao Wang

TL;DR
This paper investigates the Gallai-Ramsey numbers for double star graphs, establishing bounds and exact values in certain cases, advancing understanding of edge colorings in complete graphs.
Contribution
It provides general bounds and exact results for Gallai-Ramsey numbers of double star graphs, a new class of graphs in this context.
Findings
Established upper and lower bounds for Gallai-Ramsey numbers of double stars.
Derived sharp results for specific cases of double star graphs.
Enhanced understanding of rainbow and monochromatic subgraph occurrences in edge colorings.
Abstract
Given a graph and a positive integer , the \emph{Gallai-Ramsey number} is defined to be the minimum number of vertices such that any -edge coloring of contains either a rainbow (all different colored) copy of or a monochromatic copy of . In this paper, we obtain general upper and lower bounds on the Gallai-Ramsey numbers for double stars , where is the graph obtained from the union of two stars and by adding an edge between their centers. We also provide the sharp result in some cases.
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
