On the Ramsey numbers of fans and stars
Louis DeBiasio, Tucker Wimbish

Abstract
Let be the graph on vertices consisting of triangles meeting at a single vertex. After a number of improvements over the years, it is currently known that the Ramsey number of is between (Chen, Yu, Zhao) and (Dvo{\v{r}}{\'a}k and Metrebian). We improve both of these bounds as follows Additionally, as it relates to the lower bound on (and for which nothing was known when ), we determine the Ramsey numbers of stars vs.~fans, within a constant, as follows In particular, we have .
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