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 ...

Project for the FINP course at UL FMF. We want to find a planar subcubic graph with the packing coloring number as large as possible. We implement an ILP model to determine the packing coloring number ...

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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].

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 ...