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Strong forms of stability from flag algebra calculations
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2019 (English)In: Journal of combinatorial theory. Series B (Print), ISSN 0095-8956, E-ISSN 1096-0902, Vol. 135, p. 129-178Article in journal (Refereed) Published
Abstract [en]

Given a hereditary family g of admissible graphs and a function lambda(G) that linearly depends on the statistics of order-k subgraphs in a graph G, we consider the extremal problem of determining lambda(n, g), the maximum of lambda(G) over all admissible graphs G of order n. We call the problem perfectly B-stable for a graph B if there is a constant C such that every admissible graph G of order n >= C can be made into a blow-up of B by changing at most C(lambda(n, g) - lambda(G)) (n 2) adjacencies. As special cases, this property describes all almost extremal graphs of order n within o(n(2)) edges and shows that every extremal graph of order n >= C is a blow-up of B. We develop general methods for establishing stability-type results from flag algebra computations and apply them to concrete examples. In fact, one of our sufficient conditions for perfect stability is stated in a way that allows automatic verification by a computer. This gives a unifying way to obtain computer-assisted proofs of many new results.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 135, p. 129-178
Keywords [en]
Edit distance, Flag algebras, Stability, Subgraph count
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:umu:diva-162504DOI: 10.1016/j.jctb.2018.08.001ISI: 000455970100006OAI: oai:DiVA.org:umu-162504DiVA, id: diva2:1344717
Available from: 2019-08-21 Created: 2019-08-21 Last updated: 2019-08-21Bibliographically approved

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Sliačan, Jakub

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  • apa
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  • Other style
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  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
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  • Other locale
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  • asciidoc
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