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University of Birmingham > Talks@bham > Combinatorics and Probability seminar > Stability results for graphs containing a critical edge
![]() Stability results for graphs containing a critical edgeAdd to your list(s) Download to your calendar using vCal
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. This talk is included in these lists:Note that ex-directory lists are not shown. |
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