You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Given a collection of n rooted trees with depth h, we give a necessary and sufficient condition for this collection to be the collection of h-depth universal covering neighborhoods at each vertex.

Cited Abstract(s):
[1]: 

[2]: Seven criteria for integer sequences being graphic are listed. Being graphic means that there is a simple graph with the given integer sequence as degree sequence. One of the criteria leads to a new and constructive proof of the well-known criterion of Erdos-Gallai.

[3]: Abstract Given pairs ( a 1 , b 1 ) , … , ( a n , b n ) of nonnegative integers, the digraph realization problem for digraphs asks whether there is a simple digraph (no loops or multiple arcs) with vertices v 1 , … , v n such that each vertex v i ∈ V has indegree a i and outdegree b i . Fulkerson and Chen obtained a characterization analogous to the classical Erdős–Gallai characterization for graphs, but with the additional constraint that the pairs must be sorted in nonincreasing lexicographical order. We provide a more general characterization that avoids the additional sorting. The inequalities needed correspond to those k such that a k + 1 > a k . We prove a similar result when one loop is allowed at each vertex.
A short and constructive proof is available at [1] . In fact, the Erdös-Gallai condition is not the only sufficient and necessary condition for an integer sequence to be graphical ; there are some other (equivalent) conditions, notably listed in [2] . The corresponding realization problem for had also been solved quite early ; see the interesting note [3] for a complete history and presentation of the many variants.