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Given a vector $\\mathfrak{c}\\in\\mathbb{N}^n$, the ideal $I_{\\mathfrak{c}}$ is the ideal generated by those monomials belonging to $I$ whose exponent vectors are componentwise bounded above by $\\mathfrak{c}$. Let $\\delta_{\\mathfrak{c}}(I)$ be the largest integer $q$ for which $(I^q)_{\\mathfrak{c}}\\neq 0$. For a finite graph $G$, its edge ideal is denoted by $I(G)$. 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Given a vector $\\mathfrak{c}\\in\\mathbb{N}^n$, the ideal $I_{\\mathfrak{c}}$ is the ideal generated by those monomials belonging to $I$ whose exponent vectors are componentwise bounded above by $\\mathfrak{c}$. Let $\\delta_{\\mathfrak{c}}(I)$ be the largest integer $q$ for which $(I^q)_{\\mathfrak{c}}\\neq 0$. For a finite graph $G$, its edge ideal is denoted by $I(G)$. 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