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We show that for several pattern graphs on four vertices (e.g., C4), their induced copies in host graphs with n vertices and no clique on k + 1 vertices can be deterministically detected in time Õ (nωkμ + n2k2), where Õ (f) stands for O(f(log f)c) for some constant c, and μ ≈ 0. 46530. The aforementioned pattern graphs have a pair of non-adjacent vertices whose neighborhoods are equal. By consider
