Discussiones Mathematicae Graph Theory 26(3) (2006) 419-430
doi: 10.7151/dmgt.1334

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THE UPPER DOMINATION RAMSEY NUMBER u(4,4)

Tomasz Dzido

Department of Computer Science
University of Gdańsk
Wita Stwosza 57, 80-952 Gdańsk, Poland
e-mail: tdz@math.univ.gda.pl

Renata Zakrzewska

Department of Discrete Mathematics
Gdańsk University of Technology
G. Narutowicza 11/12, 80-952 Gdańsk, Poland
e-mail: renataz@mif.pg.gda.pl

Abstract

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.

2000 Mathematics Subject Classification: 05C15, 05C55, 05C69.

References

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Received 11 October 2005
Revised 4 July 2006