# Good edge-labelling of graphs

1 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : A {\em good edge-labelling} of a graph $G$ is a labelling of its edges such that, for any ordered pair of vertices $(x,y)$, there do not exist two paths from $x$ to $y$ with increasing labels. This notion was introduced in~\cite{BCP} to solve wavelength assignment problems for specific categories of graphs. In this paper, we aim at characterizing the class of graphs that admit a good edge-labelling. First, we exhibit infinite families of graphs for which no such edge-labelling can be found. We then show that deciding if a graph admits a good edge-labelling is NP-complete. Finally, we give large classes of graphs admitting a good edge-labelling: forests, $C_3$-free outerplanar graphs, planar graphs of girth at least 6, subcubic $\{C_3,K_{2,3}\}$-free graphs.
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Reports

Cited literature [12 references]

https://hal.inria.fr/inria-00383343
Contributor : Nathann Cohen <>
Submitted on : Friday, May 15, 2009 - 7:08:26 PM
Last modification on : Monday, October 12, 2020 - 10:30:21 AM
Long-term archiving on: : Saturday, November 26, 2016 - 9:20:45 AM

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RR-6934.pdf
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• HAL Id : inria-00383343, version 4

### Citation

Julio Araújo, Nathann Cohen, Frédéric Giroire, Frédéric Havet. Good edge-labelling of graphs. [Research Report] RR-6934, INRIA. 2009, pp.16. ⟨inria-00383343v4⟩

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