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 ...

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 ...

Barnette's Conjecture: Every 3-connected cubic planar bipartite graph is Hamiltonian. It is known that this is not true if you remove the "bipartite" condition, but the smallest 3-connected cubic ...

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections. “It’s a bit of a surprise, at least for me, that such a combination ...