Geodesic
The upper domination Ramsey number u(4,4)
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 3, pp. 419-430

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The upper domination Ramsey number u(m,n) is the smallest integer p such that every 2-coloring of the edges of Kₚ with color red and blue, Γ(B) ≥ m or Γ(R) ≥ n, where B and R is the subgraph of Kₚ induced by blue and red edges, respectively; Γ(G) is the maximum cardinality of a minimal dominating set of a graph G. In this paper, we show that u(4,4) ≤ 15.
Keywords: edge coloring, upper domination Ramsey number 
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Dzido, Tomasz; Zakrzewska, Renata. The upper domination Ramsey number u(4,4). Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 3, pp. 419-430. http://geodesic.mathdoc.fr/item/DMGT_2006_26_3_a6/