Cheeger inequalities for graph limits
Abhishek Khetan, Mahan Mj
TL;DR
This paper extends Cheeger inequalities to the setting of graph limits, specifically graphons and graphings, by defining appropriate Cheeger constants and establishing related inequalities and co-area formulas.
Contribution
It introduces Cheeger constants for graphons and graphings and proves Cheeger and Buser inequalities in this new context, along with co-area formulas.
Findings
Cheeger constants defined for graphons and graphings
Proved Cheeger and Buser inequalities for these structures
Established co-area formulas for graphons and graphings
Abstract
We introduce notions of Cheeger constants for graphons and graphings. We prove Cheeger and Buser inequalities for these. On the way we prove co-area formulae for graphons and graphings.
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Taxonomy
TopicsGraph theory and applications · Advanced Operator Algebra Research · Limits and Structures in Graph Theory