Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

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 ...

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones. On January 8, three mathematicians posted a proof of a nearly 60-year-old problem in ...