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@ -214,6 +214,8 @@ Then $\numocc{\tri}_2 = 0$, and if we can prove that
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we solve our problem for $q_E^3$ based on $G_2$ and we can compute $\numocc{\threedis}$, a hard problem.
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\end{proof}
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\AH{Proving the above linear combination for 3-matchings in $G_2$ always holds for an arbitrary $G_1$.}
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Consider graph $G_2$, constructed from an arbitrary graph $G_1$. We wish to show that the number of 3-matchings in $G_2$ will always be the linear combination above, regardless of the construction of $G_1$.
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\begin{proof}
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