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The irredundant ramsey number s(3,3,3) = 13
Author(s) -
Cockayne E. J.,
Mynhardt C. M.
Publication year - 1994
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190180607
Subject(s) - combinatorics , mathematics , ramsey's theorem , integer (computer science) , edge coloring , discrete mathematics , graph , computer science , line graph , graph power , programming language
Let G 1 , G 2 ,. …, G t be an arbitrary t ‐edge coloring of K n , where for each i ∈ {1,2, …, t }, G i is the spanning subgraph of K n consisting of all edges colored with the i th color. The irredundant Ramsey number s ( q 1 , q 2 , …, q t ) is defined as the smallest integer n such that for any t ‐edge coloring of K n , i has an irredundant set of size q i for at least one i ∈ {1,2, …, t }. It is proved that s(3,3,3) = 13, a result that improves the known bounds 12 ≤ s(3,3,3) ≤ 14.