Open AccessThe upper domination Ramsey number u(4,4)
Author(s) -
Tomasz Dzido,
Renata Zakrzewska
Publication year - 2006
Publication title -
discussiones mathematicae graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.476
H-Index - 19
eISSN - 2083-5892
pISSN - 1234-3099
DOI - 10.7151/dmgt.1334
Subject(s) - mathematics , ramsey's theorem , combinatorics , domination analysis , graph , vertex (graph theory)
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.
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