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Extremal graphs and graph limits
If you have a question about this talk, please contact Andrew Thomason.
Growing sequences of dense graphs have a limit object in terms of a symmetric measuable 2-variable function. A typical use of this fact in graph theory is the following: we want to prove a result, say an inequality between subgraph densities. We look at a sequence of counterexamples, and consider their limit. Often this allows clean formulations and arguments that would be awkward or impossible in the finite setting. We illustrate this by some results on Sidorenko’s conjecture and “common graphs”.
This setting also allows us to pose and in some cases answer general questions about extremal graph theory: which inequalities between subgraph densities are valid, and what is the possible structure of extremal graphs.
This talk is part of the Combinatorics Seminar series.
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