📐 Erdős-Gallai Theorem
A non-increasing sequence $(d_1, \\ldots, d_n)$ of non-negative integers is graphic if and only if $\\sum d_i$ is even and for each $k \\in [n]$: $\\sum_{i=1}^k d_i \\leq k(k-1) + \\sum_{i=k+1}^n \\min(d_i, k)$.
From: Introduction to Graph Theory
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