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We note that previous work on degrees and factors has focused primarily on finding conditions for a degree sequence to be potentially $k$-factor graphical.\n  We first give a theorem for $\\pi$ to be forcibly 1-factor graphical and, more generally, forcibly graphical with deficiency at most $\\beta\\ge0$. These theorems are equal in strength to Chv\\'atal's well-known hamiltonian theorem, i.e., the best monotone degree condition for hamiltonicity. 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