The Γ-switch Ramsey number is defined and shown to satisfy R_{C3}(4,4,4) = R(3,3,3) + 1, R_{C4}(3,4,3,4) = R(2,3,2,3) + 1, and 43 ≤ R_{C4}(4,4,4,4) ≤ R(3,3,3,3) + 1.
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The Gamma-Switch Ramsey Number
The Γ-switch Ramsey number is defined and shown to satisfy R_{C3}(4,4,4) = R(3,3,3) + 1, R_{C4}(3,4,3,4) = R(2,3,2,3) + 1, and 43 ≤ R_{C4}(4,4,4,4) ≤ R(3,3,3,3) + 1.