Tag Archives: extremal problems

A short video on Ramsey numbers

I was recently involved in making a 1 minute maths video for a contest organised by Veritasium. Here is the main requirement for the video We are looking for videos that clearly and creatively explain complex or counterintuitive concepts in … Continue reading

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The dual version of Ryser’s conjecture

I talked about our new results related to Ryser’s conjecture in a previous post (also see an even earlier post). The conjecture, and its variants, have some interesting equivalent formulations in terms of edge colourings of graphs. While I was … Continue reading

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Generalized polygons in extremal combinatorics

Jacques Tits invented generalized polygons to give a geometrical interpretation of the exceptional groups of Lie type. The prototype of these incidence geometries already appears in his 1956 paper, while they are axiomatically defined in his influential 1959 paper on … Continue reading

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Bounds on Ramsey numbers from finite geometry

In an earlier post I talked about the work of Mubayi and Verstraete on determining the off-diagonal Ramsey numbers via certain optimal pseudorandom graphs, which are not yet known to exist except for the case of triangles. Beyond this conditional … Continue reading

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Wenger graphs

A central (and foundational) question in extremal graph theory is the forbidden subgraph problem of Turán, which asks for the largest number of edges in an -vertex graph that does not contain any copy of a given graph as its … Continue reading

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On a famous pigeonhole problem

After a short break from blogging, which involved moving from Ghent to Berlin, dealing with German bureaucracy, and learning how to make simple websites (the easiest bit), I am now back. I am working as a postdoc at the Free … Continue reading

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