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An Arboricity-Sensitive Algorithm for the $K_r-e$-Free Graph Sandwich Problem
For a fixed integer $r\geq4$, the $K_r-e$-free graph sandwich problem asks whether, given graphs $G_1\subseteq G_2$ on the same vertex set, there is an induced-$K_r-e$-free graph $H$ between them. We give a deterministic algorithm taking $O(n+α(G_2)^{r-3}m_2)$ time and space, where $m_2=|E(G_2)|$ an
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