Babai's talks sketch a proof that shows that the graph isomorphism problem — determining whether two graphs are the same — can be solved much more quickly than was previously known.

But already in 1980, another classical theorem—the Babai-Erdős-Selkow theorem—showed that almost all graphs can be relabeled to make easy isomorphism testing possible.

For decades, the graph isomorphism problem has held a special status within complexity theory. While thousands of other computational problems have meekly succumbed to categorization as either ...

We show that the groupoids of two directed graphs are isomorphic if and only if the two graphs are orbit equivalent by an orbit equivalence that preserves isolated eventually periodic points. We also ...

Computer Science Landmark Algorithm Breaks 30-Year Impasse Computer scientists are abuzz over a fast new algorithm for solving one of the central problems in the field. The “graph isomorphism” ...

Abstractions blog Complexity Theory Problem Strikes Back The legendary graph isomorphism problem may be harder than a 2015 result seemed to suggest. Lucy Reading-Ikkanda for Quanta Magazine The ...

Solving sudoku puzzles may not require mathematics, but mathematicians have found plenty to say about the popular brainteasers.

We present an overview of basic elements of graph theory as it might be applied to issues of connectivity in heterogeneous landscapes, focusing especially on applications of metapopulation theory in ...