The upper domination Ramsey number u(4,4)

Tomasz Dzido; Renata Zakrzewska

Discussiones Mathematicae Graph Theory (2006)

  • Volume: 26, Issue: 3, page 419-430
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Tomasz Dzido, and Renata Zakrzewska. "The upper domination Ramsey number u(4,4)." Discussiones Mathematicae Graph Theory 26.3 (2006): 419-430. <http://eudml.org/doc/270162>.

@article{TomaszDzido2006,
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.},
author = {Tomasz Dzido, Renata Zakrzewska},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {edge coloring; upper domination Ramsey number},
language = {eng},
number = {3},
pages = {419-430},
title = {The upper domination Ramsey number u(4,4)},
url = {http://eudml.org/doc/270162},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Tomasz Dzido
AU - Renata Zakrzewska
TI - The upper domination Ramsey number u(4,4)
JO - Discussiones Mathematicae Graph Theory
PY - 2006
VL - 26
IS - 3
SP - 419
EP - 430
AB - 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.
LA - eng
KW - edge coloring; upper domination Ramsey number
UR - http://eudml.org/doc/270162
ER -

References

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  1. [1] R.C. Brewster, E.J. Cockayne and C.M. Mynhardt, Irredundant Ramsey numbers for graphs, J. Graph Theory 13 (1989) 283-290, doi: 10.1002/jgt.3190130303. Zbl0686.05038
  2. [2] E.J. Cockayne, G. Exoo, J.H. Hattingh and C.M. Mynhardt, The Irredundant Ramsey Number s(4,4), Util. Math. 41 (1992) 119-128. Zbl0771.05070
  3. [3] E.J. Cockayne and S.T. Hedetniemi, Towards a theory of domination in graphs, Networks 7 (1977) 247-261, doi: 10.1002/net.3230070305. Zbl0384.05051
  4. [4] R.E. Greenwood and A.M. Gleason, Combinatorial relations and chromatic graphs, Canadian J. Math. 7 (1955) 1-7, doi: 10.4153/CJM-1955-001-4. Zbl0064.17901
  5. [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs, Marcel Dekker, New York, (1998) (Proposition 3.8, p. 72). Zbl0890.05002
  6. [6] M.A. Henning and O.R. Oellermann, The upper domination Ramsey number u(3,3,3), Discrete Math. 242 (2002) 103-113, doi: 10.1016/S0012-365X(00)00369-1. Zbl0994.05093
  7. [7] M.A. Henning and O.R. Oellermann, On upper domination Ramsey numbers for graphs, Discrete Math. 274 (2004) 125-135, doi: 10.1016/S0012-365X(03)00084-0. Zbl1037.05034

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