@article{, AUTHOR = {Dzido, Tomasz and Zakrzewska, Renata}, TITLE = {The upper domination Ramsey number $u(4,4)$}, JOURNAL = {Discuss. Math. Graph Theory}, FJOURNAL = {Discussiones Mathematicae Graph Theory}, VOLUME = {26}, YEAR = {2006}, NUMBER = {3}, PAGES = {419-430}, ISSN = {1234-3099}, ABSTRACT = {The upper domination Ramsey number $u(m,n)$ is the smallest integer $p$ such that every $2$-coloring of the edges of $K_p$ with color red and blue, $\Gamma(B)\geq m$ or $\Gamma(R)\geq n,$ where $B$ and $R$ is the subgraph of $K_p$ induced by blue and red edges, respectively; $\Gamma(G)$ is the maximum cardinality of a minimal dominating set of a graph $G$. In this paper, we show that $u(4,4)\leq 15$.},}