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Lemma 55.5.6. Nonexistence of proper subgraphs of the form

\[ \xymatrix{ \bullet \ar@{-}[r] & \bullet \ar@{-}[ld] \ar@{-}[r] \ar@{-}[d] & \bullet \\ \bullet & \bullet } \]

If $n > 5$, there do not exist five $(-2)$-indices $h$, $i$, $j$, $k$ with $a_{hi} > 0$, $a_{hj} > 0$, $a_{hk} > 0$, and $a_{hl} > 0$.

Proof. See discussion above. $\square$

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