Lemma 55.5.11. Nonexistence of proper subgraphs of the form
\[ \xymatrix{ \bullet \ar@{-}[r] & \bullet \ar@{..}[r] \ar@{-}[d] & \bullet \ar@{-}[d] \ar@{-}[r] & \bullet \\ & \bullet & \bullet } \]
Assume $t \geq 4$ and $n > t + 2$. There do not exist $t + 2$ distinct $(-2)$-indices $i_0, \ldots , i_{t + 1}$ such that $a_{i_ ji_{j + 1}} > 0$ for $j = 1, \ldots , t - 1$ and $a_{i_0i_2} > 0$ and $a_{i_{t - 1}i_{t + 1}} > 0$.
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