FIG. 3: Positions of the gluons corresponding to the two gravitons ( N + 1)$_{h}$ and ( N + 2)$_{h}$ for (a) 1 < l < i , (b) i < l ≤ N in B part. respectively. Then for any given k , each term in the second line of (25) insert the two gluons corresponding to ( N + 1)$_{h}$ at the positions between 1, k and k , i respectively. The C part then becomes where P$_{3}$ are the insertions of the four gluons corresponding to the two gravitons ( N + 2)$_{h}$ and ( N + 1)$_{h}$. In these insertions, two gluons corresponding to ( N + 2)$_{h}$ are inserted at the positions between 1, l and l , i respectively, then two gluons corresponding to ( N + 1)$_{h}$ are inserted at the positions between 1, k and k , i respectively( See Fig. 4). After considering all the contributions from A , B and C , we give the D$_{2}$ relation C = ∑ l,k ∈ g + s$_{l,N}$$_{+2}$s$_{k,N}$$_{+1}$ ∑ P$_{3}$ A N +4 $_{MHV}$( P$_{3}$ ) . (31) A (1 − g , 2 + g , ..., i − g , ..., N + g , ( N + 1) + $_{h}$, ( N + 2) + $_{h}$) = ∑ l ∈{ g $^{+}$} s$_{l,N}$$_{+1}$s$_{N}$$_{+1}$$_{,N}$$_{+2}$ ∑ P$_{1}$ A N +4 $_{MHV}$( P$_{1}$ ) + ∑ l ∈{ g $^{+}$} s$_{l,N}$$_{+2}$s$_{N}$$_{+2}$$_{,N}$$_{+1}$ ∑ P$_{2}$ A N +4 $_{MHV}$( P$_{2}$ ) + ∑ l,k ∈ g + s$_{l,N}$$_{+2}$s$_{k,N}$$_{+1}$ ∑ P$_{3}$ A N +4 $_{MHV}$( P$_{3}$ ) . (32) 19