Stability for maximal independent sets
Jeff Kahn, Jinyoung Park
TL;DR
This paper establishes stability results for upper bounds on the number of maximal independent sets in graphs, showing that near-maximal counts imply the presence of large specific matchings.
Contribution
It provides new stability theorems linking maximal independent set counts to large induced matchings or triangle matchings under various graph restrictions.
Findings
Near-maximal independent set counts imply large induced matchings.
Stability results hold under various graph restrictions.
Answers to questions posed by Y. Rabinovich.
Abstract
Answering questions of Y. Rabinovich, we prove "stability" versions of upper bounds on maximal independent set counts in graphs under various restrictions. Roughly these say that being close to the maximum implies existence of a large induced matching or triangle matching (depending on assumptions).
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