Cubic graphs – those regular graphs in which every vertex has degree three – remain a fertile area of research in both combinatorics and theoretical computer science. These graphs are not only central ...

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 ...

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Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg—an associate professor in the department of applied mathematics and computer science at the ...

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 ...

Abstract. If X is a geodesic metric space and 𝑥₁, 𝑥₂, 𝑥₃ ∈ 𝑋, a geodesic triangle 𝑇 = {𝑥₁, 𝑥₂, 𝑥₃} is the union of the three geodesics [𝑥₁𝑥₂], [𝑥₂𝑥₃] and [𝑥₃𝑥₁] in 𝑋. The space 𝑋 is ...

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 ...