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 $u(4,4)\leq 15$.},