Someone finally solved a math puzzle that was so messy, the most famous mathematician of the last century just gave up and called it 'too complicated.'
April 13, 2026
Original Paper
On the chromatic profile for tripartite graphs and beyond
arXiv · 2604.09394
The Takeaway
Paul Erdős, a legendary figure who solved thousands of problems, labeled this specific graph-theory puzzle as essentially unsolvable due to its complexity. By finding a neat, finite set of answers, these researchers have cleared a hurdle that one of history's greatest minds thought was impossible to jump.
From the abstract
Let $H$ be a graph and let $\delta_{\chi}(H,r)$ denote the infimum of $c$ such that every $H$-free graph with minimum degree at least $cn$ is $r$-colorable. The \textit{chromatic profile} of $H$ is defined to be the values of $\delta_{\chi}(H,r)$ as $r$ varies. Erdős and Simonovits described this graph parameter as ``too complicated", and Allen, Böttcher, Griffiths, Kohayakawa, and Morris posed its determination for every graph $H$ as an open problem \cite[Problem~45]{ABGKM2013}, emphasizing its