On Some Ramsey Numbers for Quadrilaterals Versus Wheels

The anti-Ramsey number AR(Kn, H) was introduced by Erdźs, Simonovits and Sós in 1973, which is defined to be the maximum number of colors in an edge coloring of the complete graph Kn without any rainbow H. Later, the anti-Ramsey numbers for several ...

For given simple graphs $G_1$ and $G_2$, the size Ramsey number $\hat{R}(G_1,G_2)$ is the smallest positive integer $m$, where there exists a graph $G$ with $m$ edges such that in any edge coloring of $G$ with two colors red and blue, there is either a ...

In this paper, we consider an extension of cycle-complete graph Ramsey numbers to Berge cycles in hypergraphs: for $k \geq 2$, a nontrivial Berge $k$-cycle is a family of sets $e_1,e_2,\dots,e_k$ such that $e_1 \cap e_2, e_2 \cap e_3,\dots,e_k \cap e_1$ ...