Forbidden subgraphs for constant domination number

In this paper, we characterize the sets $\mathcal{H}$ of connected graphs such that there exists a constant $c=c(\mathcal{H})$ satisfying $\gamma (G)\leq c$ for every connected $\mathcal{H}$-free graph $G$, where $\gamma (G)$ is the domination number of $G$.Comment: 6 pages, 1 figur

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.Comment: 12 pages, 1 figures

Forbidden subgraphs for constant domination number

In this paper, we characterize the sets $\mathcal{H}$ of connected graphs such that there exists a constant $c=c(\mathcal{H})$ satisfying $\gamma (G)\leq c$ for every connected $\mathcal{H}$-free graph $G$, where $\gamma (G)$ is the domination number of $G$