Graphs are everywhere. In discrete mathematics, they are structures that show the connections between points, much like a public transportation network. Mathematicians have long sought to develop ...

Just five days after posting a retraction, László Babai announced that he had fixed the error in his landmark graph isomorphism algorithm. The back and forth ...

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 ...

A puzzle that has long flummoxed computers and the scientists who program them has suddenly become far more manageable. A new algorithm efficiently solves the graph isomorphism problem, computer ...

It is well known that two structures are $L_{\infty\omega}$-equivalent $\operatorname{iff}$ they are potentially isomorphic [that is, isomorphic in some (Cohen ...

Computer scientists are abuzz over a fast new algorithm for solving one of the central problems in the field. (January 15, 2017, update: On January 4, Babai retracted his claim that the new algorithm ...

Forbes contributors publish independent expert analyses and insights. I help people communicate data clearly with graphs. If you are looking for examples of misleading or deceptive graphs, it is far ...