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 ...

In 1852, botanist Francis Guthrie noticed something peculiar as he was coloring a map of counties in England. Despite the counties’ meandering shapes and varied configurations, four colors were all he ...

Among the 23 remarkable individuals who won MacArthur Foundation fellowships earlier this week, there was mathematician Maria Chudnovsky, who is married to a violist, and stringed instrument bow-maker ...

A new proof has debunked a conspiracy that mathematicians feared might haunt the number line. In doing so, it has given them another set of tools for understanding arithmetic’s fundamental building ...

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 ...