Tools for parsimonious edge-colouring of graphs with maximum degree three
Jean-Luc Fouquet (LIFO), Jean-Marie Vanherpe (LIFO)

TL;DR
This paper explores structural properties of $oldsymbol{ ext{delta}}$-minimum edge-colourings in graphs with maximum degree three, providing tools that facilitate efficient edge-colouring in such graphs.
Contribution
It introduces structural insights into $oldsymbol{ ext{delta}}$-minimum edge-colourings, aiding future research and applications in graph colouring.
Findings
Identifies key structural properties of $oldsymbol{ ext{delta}}$-minimum edge-colourings.
Provides auxiliary tools for edge-colouring algorithms.
Supports further research in graph colouring with maximum degree three.
Abstract
The notion of a -minimum edge-colouring was introduced by J-L. Fouquet (in his french PhD Thesis \cite{FouPhD}). Here we present some structural properties of -minimum edge-colourings, partially taken from the above thesis. The paper serves as an auxiliary tool for another paper submitted by the authors to Graphs and Combinatorics.
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Taxonomy
TopicsAdvanced Graph Theory Research · graph theory and CDMA systems · Limits and Structures in Graph Theory
