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 ...

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 ...

If true, the following conjecture of Thomassen [Th81] is a planarity criterion for a special class of graphs that involves only K 5. Recall that a planar graph on n vertices contains at most 3n-6 ...

Perold, André, V. Chvatal, R. L. Graham, and S. Whitesides. "Combinatorial Designs Related to the Strong Perfect Graph Conjecture." Discrete Mathematics 26, no. 2 ...

Let G be a locally finite infinite graph and let I(G) be the set of ends of G. The Freudenthal compactification of G is the topological space |G| which is obtained from the usual topological space of ...

An artificial intelligence has disproved five mathematical conjectures – unproven theorems – despite not being equipped with any information about the problems. Adam Zsolt Wagner at Tel Aviv ...