University of Birmingham > Talks@bham > Combinatorics and Probability Seminar > The minimum number of triangles in a graph of given order and size

The minimum number of triangles in a graph of given order and size

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  • UserKatherine Staden (University of Oxford)
  • ClockTuesday 20 February 2018, 15:00-16:00
  • HousePhysics West 106.

If you have a question about this talk, please contact Allan Lo.

A famous theorem of Mantel from 1907 states that every n-vertex graph with more than n^2/4 edges contains at least one triangle. In the 50s, Erdős asked for a quantitative version of this statement: for every n and e, how many triangles must an n-vertex e-edge graph contain? This question has received a great deal of attention, and a long series of partial results culminated in an asymptotic solution by Razborov, extended to larger cliques by Nikiforov and Reiher. Until recently, an exact solution was only known for a small range of edge densities, due to Lovász and Simonovits. In this talk, I will discuss the history of the problem and some new work which gives an exact solution for almost the entire range of edge densities. This is joint work with Hong Liu and Oleg Pikhurko.

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

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