Turán(1941)determined the Turán number ex(n,Kp)for p≥3.Moon(1968)and Simonovits(1968)independently determined the Turán number ex(n,kKp)for n sufficiently large,and determined that Kk-1 ∨Tp-1(n-k+1)is the unique extremal graph for kKp.Chen et al.(2022)showed the exact value of ex(n,2Kp)for all n ≥ 2p and p ≥ 3.In this paper,we determine ex(n,3Kp)for all n≥3p and determine extremal graphs for 3Kp.Determining Turán numbers ex(n,F)under the condition n large enough cannot be applied to corresponding Ramsey numbers.The result in this paper can be applied to determining the Ramsey number R(3Kp,Pt)for t≥ 6 and p≥3.
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