For a whiskered cycle G = W(C_n), the regularity of its q-th squarefree edge ideal power is exactly 2q + floor((n - q - 1)/2) for q up to the matching number.
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Regularity of Squarefree Powers of Edge Ideals of Whiskered Cycles
For a whiskered cycle G = W(C_n), the regularity of its q-th squarefree edge ideal power is exactly 2q + floor((n - q - 1)/2) for q up to the matching number.