Compact graphings

Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. A graphing is compact, if the underlying space is a compact metric space, the edge set is closed and nearby points have nearby graph neighbo...

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Veröffentlicht in:	Acta mathematica Hungarica 2020-06, Vol.161 (1), p.185-196
1. Verfasser:	Lovasz, L.
Format:	Artikel
Sprache:	eng
Schlagworte:	Graphical representations Mathematics Mathematics and Statistics Metric space Physical Sciences Science & Technology
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. A graphing is compact, if the underlying space is a compact metric space, the edge set is closed and nearby points have nearby graph neighborhoods. We prove some simple properties of compact graphings. Our main result is a procedure for embedding an arbitrary graphing into an essentially equivalent compact graphing.
ISSN:	0236-5294 1588-2632
DOI:	10.1007/s10474-019-01010-8