There is a philosophy to discover Ramsey-type theorem: given a graph
parameter μ, characterize the family \HH of graphs which satisfies that
every \HH-free graph G has bounded parameter μ. The classical Ramsey's
theorem deals the parameter μ 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.Comment: 12 pages, 1 figures