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- W4296765183 abstract "Given a hereditary family $mathcal{G}$ of admissible graphs and a function $lambda(G)$ that linearly depends on the statistics of order-$kappa$ subgraphs in a graph $G$, we consider the extremal problem of determining $lambda(n,mathcal{G})$, 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 $nge C$ can be made into a blow-up of $B$ by changing at most $C(lambda(n,mathcal{G})-lambda(G)){nchoose2}$ 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 $nge n_0$ 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." @default.
- W4296765183 created "2022-09-23" @default.
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- W4296765183 date "2017-06-08" @default.
- W4296765183 modified "2023-09-27" @default.
- W4296765183 title "Strong Forms of Stability from Flag Algebra Calculations" @default.
- W4296765183 doi "https://doi.org/10.48550/arxiv.1706.02612" @default.
- W4296765183 hasPublicationYear "2017" @default.
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