Abstract
Let \(A_n=(a_1,a_2,\ldots ,a_n)\) and \(B_n=(b_1,b_2,\ldots ,b_n)\) be nonnegative integer sequences with \(A_n\le B_n\). The purpose of this note is to give a good characterization such that every integer sequence \(\pi =(d_1,d_2,\ldots d_n)\) with even sum and \(A_n\le \pi \le B_n\) is graphic. This solves a forcible version of problem posed by Niessen and generalizes the Erdős–Gallai theorem.
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