Mixed, Multi-color, and Bipartite Ramsey Numbers Involving Trees of Small Diameter
Jeremy F. Alm, Nicholas Hommowun, Aaron Schneider
TL;DR
This paper investigates Ramsey numbers involving small-diameter trees, providing exact values and growth rates for bipartite multi-color Ramsey numbers related to bistars, stars, and complete graphs.
Contribution
It determines exact Ramsey numbers for bistars versus complete graphs and analyzes the growth of bipartite k-color Ramsey numbers for bistars.
Findings
Exact Ramsey numbers for bistars vs. complete graphs
Order of growth for bipartite k-color Ramsey numbers of bistars
Relationships between small-diameter trees and classical Ramsey numbers
Abstract
In this paper we study Ramsey numbers for trees of diameter 3 (bistars) vs., respectively, trees of diameter 2 (stars), complete graphs, and many complete graphs. In the case of bistars vs. many complete graphs, we determine this number exactly as a function of the Ramsey number for the complete graphs. We also determine the order of growth of the bipartite -color Ramsey number for a bistar.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Advanced Topology and Set Theory