Ramsey Goodness of paths and unbalanced graphs
Ramsey Goodness of paths and unbalanced graphs
Given graphs $G$ and $H$, we say that $G$ is $H$-$good$ if the Ramsey number $R(G,H)$ equals the trivial lower bound $(|G| - 1)(\chi(H) - 1) + \sigma(H)$, where $\chi(H)$ denotes the usual chromatic number of $H$, and $\sigma(H)$ denotes the minimum size of a color class in a $\chi(H)$-coloring …