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# Math insight

Mathematicians can be fascinated by the elegance and beauty of the ideas behind mathematical theories. Mathematical structures are already out there and our goal is to discover them.

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### 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.
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### 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.
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### 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.