## Does no small structure mean larger homogeneous ones?

A conjecture of Erdős and Hajnal from 1989 says that forbidding any specific substructure results in existence of a very large homogeneous one! In this article you will have a look into one of the most fascinating problems in modern graph theory.

## Picking up 13 different cards from 13 piles (Part 2)

In Part 1 Jackie explained to her fried Sam how the problem of picking a card from each of the 13 piles so that there is exactly one card with each rank translates to a problem on bipartite graphs. The mathematical problem asks you to find a perfect matching in a regular bipartite graph.

## Picking up 13 different cards from 13 piles (Part 1)

Did you know that if you divide a pack of cards into 13 piles of 4 cards, then you can always pick one card from each of the 13 piles so that there is exactly one card with each rank? There is some beautiful math behind this puzzle.

## Structure is everywhere. So is chaos.

Pick 45 numbers between 1 and 100. Try to avoid creating pairs whose difference is the square of some number and you will fail. Always.

## Centrality measures: who is the most important in a network?

In this article, we discuss several ways to quantify the importance of nodes in a network. We will discuss how a simple game can help study this special property, and how it can help us in cases like reducing fake news.

## Is it easier to find half a needle than a full needle in a random network?

Common sense tells us that objects of comparable size should be equally hard to find. Yet, when searching inside a random network, surprises are awaiting . . .

## New breakthrough about Ramsey numbers?

In a seminar talk in Cambridge this week, Julian Sahasrabudhe announced that he, together with his colleagues Marcelo Campos, Simon Griffiths and Rob Morris, had obtained an exponential improvement to the upper bound for Ramsey's theorem.

## Playing with Colors Part 2: An open problem related to graph colouring

Mathematicians often enjoy playing around with the concept of infinity and in the following, I will describe a problem defined on an infinite graph!

## Playing with Colors

Part 1: Learn about applied and theoretical aspects of graph coloring: a tool that helps us design exam schedules or even solve Sudoku!

## Let me tell you a story from my teaching

On Wednesday I was teaching an exercise class on graph theory. There was this one exercise that was troubling me for a couple of days, I couldn't solve it and it was frustrating.