University of Birmingham > Talks@bham > Combinatorics and Probability Seminar > Stability results for graphs containing a critical edge

Stability results for graphs containing a critical edge

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  • UserAlex Roberts (University of Oxford)
  • ClockThursday 28 February 2019, 13:00-14:00
  • HouseWatson LTB.

If you have a question about this talk, please contact Richard Montgomery.

The classical stability theorem of Erd\H{o}s and Simonovits states that, for any fixed graph H with chromatic number k+1 \ge 3, the following holds: every n-vertex graph that is H-free and has within o(n2) of the maximal possible number of edges can be made into the k-partite Tur\’{a}n graph by adding and deleting o(n2) edges. We prove sharper quantitative results for graphs H with a critical edge, showing how the o(n^2) terms depend on each other. In many cases, these results are optimal to within a constant factor. We also discuss other recent results in a similar vein and some motivation for providing tighter bounds.

This talk is part of the Combinatorics and Probability Seminar series.

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