Graph Polynomial: An algebraic expression that encodes key combinatorial properties of a graph. Tutte Polynomial: A two-variable polynomial invariant capturing a wide range of graph properties, ...

Two mathematicians have used a new geometric approach in order to address a very old problem in algebra. In school, we often learn how to multiply out and factor polynomial equations like (x² ...

Babai’s new result says that solving graph isomorphism takes slightly longer than polynomial time – not quite placing it in P, but significantly shifting the needle for the first time.

Chromatic Number: The minimum number of colours required to achieve a proper colouring of a graph. NP-hard: A classification for problems for which no known polynomial-time algorithm exists ...

Babai’s proposed algorithm doesn’t bring graph isomorphism all the way into P, but it comes close. It is quasi-polynomial, he asserts, which means that for a graph with n nodes, the algorithm’s ...