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 ...

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].

Learn how to draw and interpret quadratic, cubic and exponential graphs and how to use quadratic graphs to solve equations.

Then the dual cubic graph is 3-edge-colorable. Let me observe that the dual of the complete graph K6 embedded in the projective plane is the Petersen graph. I would dare to conjecture that this is the ...