Abstract
Let G be a finite, simple, and undirected graph of order n and average degree d. Up to terms of smaller order, we characterize the minimal intervals I containing d that are guaranteed to contain some vertex degree. In particular, for d+∈(dn,n−1], we show the existence of a vertex in G of degree between d+−((d+−d)nn−d++d+2−dn) and d+.
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