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: This work examines the possibilities of increasing the efficiency of the computation of proper edge k-coloring of cubic graph with the use of machine learning methods. State-of-the-art ...

An embedding of a graph G in some surface is said to be polyhedral if every facial boundary is a cycle in the graph and any two distinct faces share at most a vertex or an edge in their boundaries. It ...

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 ...