A network of 10 points and 15 lines keeps breaking mathematicians' favorite conjectures
Picture a small network of exactly 10 points, each connected to exactly 3 others, drawn so that it looks like a five-pointed star inside a pentagon, with spokes connecting the two shapes. Why would mathematicians single out this one particular arrangement, out of countless possible small networks, as worth naming and studying for over a century?
Reveal the answer
This network, the Petersen graph, keeps turning up as the smallest possible counterexample to otherwise-plausible conjectures in graph theory, disproving general claims by being the one stubborn exception. Julius Petersen first described it in an 1898 paper on graph factorization, and it has served ever since as mathematicians' go-to test case for checking whether a new graph theory idea actually holds up.
— Julius Petersen, Sur le théorème de Tait — L'Intermédiaire des Mathématiciens, 1898