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 ...

Back in the hazy olden days of the pre-2000s, navigating between two locations generally required someone to whip out a paper map and painstakingly figure out the most optimal route between those ...

An innovative approach to solving a stubborn, but elementary, question in graph theory — the mathematical study of networks of nodes and their connections — may signal the first major theoretical ...

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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 ...

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 ...

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 ...

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks — vertices (dots) and edges (lines connecting them) — has been an invaluable way ...