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A Computer-Assisted Proof that R(5,10;5,8)=21 for the Generalized Threshold Ramsey Number
We prove that the generalized threshold Ramsey number R(5,10;5,8) equals 21. This number corresponds to the set Ramsey number r_5(10,8) introduced by Harborth. The proof is computer-assisted. We first enumerate all (4,6;5,8)-good and (5,10;4,4)-good graphs. Then we apply the lucky-vertex inequality
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