se(）-68 X=∑Xs otherwise. s∈() Goal:p=(n20=o(1) Var X Prx=O≤PrIX-EIXI≥EXWI≤EX2 1 ∑s≠TCov(Xs,XT) X EX] E[X]2 Var[X]<E[X]+Cov(Xs;XT) S≠T
XS = 1 S is a clique, 0 otherwise. Goal: 8S 2 ✓[n] k ◆ X = X S2( [n] k ) XS p = ! Pr[X = 0] = o(1) ⇣ n2/(k1)⌘ Pr[X = 0] Pr[ |X E[X]| E[X] ] Var[X] Var[X] E[X] 2 1 E[X] + P S6=T Cov(XS, XT) E[X] 2 E [X] + X S6=T Cov(XS, XT )
sc(因)-{6n X= ∑ XS otherwise. s∈() Goalk:p=(n2-)=(1) PH=≤ 1 ∑s≠TCov(Xs,XT) E[X]2 x=x1-(（）p S∈() Cov(Xs,XT)=EXsXT]-E[Xs E[XT] ≤XsXr]=p2()-(s9)
XS = 1 S is a clique, 0 otherwise. Goal: 8S 2 ✓[n] k ◆ X = X S2( [n] k ) XS p = ! Pr[X = 0] = o(1) ⇣ n2/(k1)⌘ Pr[X = 0] 1 E[X] + P S6=T Cov(XS, XT) E[X] 2 E[X] = X S2( [n] k ) E [XS] = ✓n k ◆ p( k 2) E[XSXT ] Cov(XS, XT )= E[XSXT ] E[XS]E[XT ] p2( k 2)( |S\T | 2 ) =