Ramsey Goodness of paths and unbalanced graphs

Fábio Botler, Luiz Moreira, João Pedro de Souza

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 ch…