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 ...

Abstract: Proper edge 3-coloring of a cubic graph is an NP-complete problem, which is present in number of real-live problems − correct and efficient assigning of variables used in the program to ...

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].