TL;DR
This paper proves that any weakly convergent sequence of finite graphs with bounded degrees has a topological limit graphing, establishing a fundamental connection between finite graph sequences and their infinite limits.
Contribution
It introduces the existence of a topological limit graphing for weakly convergent finite graph sequences with bounded degrees, advancing the understanding of graph limits.
Findings
Existence of topological limit graphings for graph sequences
Weak convergence implies a topological limit in bounded degree graphs
Bridges finite graph sequences and infinite graphings
Abstract
We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Graph theory and applications · Advanced Graph Theory Research