Further results on strong edge-colourings in outerplanar graphs
Valentin Borozan, Leandro Montero, Narayanan Narayanan
TL;DR
This paper provides formulas and algorithms for determining the strong chromatic index of bipartite outerplanar graphs and offers improved bounds for all outerplanar graphs, advancing understanding of strong edge-colourings.
Contribution
It introduces a formula for the strong chromatic index of bipartite outerplanar graphs and improves bounds for general outerplanar graphs, with efficient algorithms for construction.
Findings
Formulas for optimal or near-optimal strong chromatic index in bipartite outerplanar graphs
An improved upper bound for the strong chromatic index of outerplanar graphs
Efficient algorithms for constructing strong edge-colourings
Abstract
An edge-colouring is {\em strong} if every colour class is an induced matching. In this work we give a formulae that determines either the optimal or the optimal plus one strong chromatic index of bipartite outerplanar graphs. Further, we give an improved upper bound for any outerplanar graph which is close to optimal. All our proofs yield efficient algorithms to construct such colourings.
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Taxonomy
TopicsAdvanced Graph Theory Research · Nuclear Receptors and Signaling · Graph Labeling and Dimension Problems