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, ...

Semigroups of transformations and endomorphisms have emerged as powerful algebraic frameworks to elucidate the underlying structures of graphs. By harnessing the principles of semigroup theory, ...

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon. When you walk into a room full of people, you can ...

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 ...