The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Main Topics: There are graphs with large chromatic number but no small cycles, Tutte’s construction, Edge-Ramsey for graphs (using partite construction)

Math is many things: beautiful, fundamental, universal, but ultimately, math is hard. So hard in fact that mathematicians often need to phone up their other mathematician friends for help. The idea of the crazy-maned recluse furiously working in his office alone is an outdated one. While some modern mathematicians still fit this bill, collaboration is increasingly the norm. By the year 2000, the number of mathematics papers with a single author had shrunk to 50%. More and more people are tackling difficult math problems as a team.

No one embodies the idea of mathematical collaboration more than Paul Erdös (pronounced err-desh or air-dish), a Hungarian mathematician who lived in the twentieth century. A legendary figure in mathematics, Erdös published around 1500 papers and had around 500 co-authors. To contrast, most mathematicians write 7 papers in their entire life! Erdös was heavily in support of working together to solve math problems and questions, and also had incredible mathematical taste. He asked very interesting questions and would often attach a dollar amount to the questions. If you were clever enough to solve one of these Erdös questions, Paul Erdös himself would send you a cheque. These cheques were so revered in mathematics that often people frame them rather than cash them. More information on his very interesting life is available here.