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 ...

Conjecture (Berge and Fulkerson): Every 2-connected cubic graph has a collection of six perfect matchings that together cover every edge exactly twice. This conjecture is attributed to Berge in [2].

Plotting a graph takes time. Often mathematicians just want to know the key features. These are: shape, location and some key points (such as where the graph crosses the axes or turning points). So ...