Ramsey-type results on parameters related to domination
There is a philosophy to discover Ramsey-type theorem: given a graph parameter $\mu$, characterize the family $\HH$ of graphs which satisfies that every $\HH$-free graph $G$ has bounded parameter $\mu$. The classical Ramsey's theorem deals the parameter $\mu$ as the number of vertices. It also has a corresponding connected version. This Ramsey-type problem on domination number has been solved by Furuya. We will use this result to handle more parameters related to domination.