Let G = (V(G), E(G)) be a graph. A set S ⊆ E(G) is an edge k-cut in G if the graph G − S = (V(G), E(G) \ S) has at least k connected components. The generalized k-edge connectivity of a graph G, ...

Anti-Ramsey theory in graphs is a branch of combinatorial mathematics that examines the conditions under which a graph, when its edges are coloured, must necessarily contain a ‘rainbow’ subgraph – a ...

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible. A paper posted online last month has disproved a ...

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 ...