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On a graph labelling conjecture involving coloured labels

Julien Bensmail 1
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : In this work, we investigate a recent conjecture by Baudon, Bensmail, Davot, Hocquard, Przybyło, Senhaji, Sopena and Woźniak, which states that graphs, in general, can be edge-labelled with red labels 1,2 and blue labels 1,2 so that every two adjacent vertices are distinguished accordingly to either the sums of their incident red labels or the sums of their incident blue labels. To date, this was verified for several classes of graphs. Also, it is known how to design several labelling schemes that are very close to what is desired. In this work, we adapt two important proofs of the field, leading to some progress towards that conjecture. We first prove that graphs can be labelled with red labels 1,2,3 and blue labels 1,2 so that every two adjacent vertices are distinguished as required. We then verify the conjecture for graphs with chromatic number at most 4.
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https://hal.archives-ouvertes.fr/hal-02554102
Contributor : Julien Bensmail <>
Submitted on : Friday, April 24, 2020 - 11:55:27 PM
Last modification on : Tuesday, May 26, 2020 - 6:50:53 PM

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Julien Bensmail. On a graph labelling conjecture involving coloured labels. [Research Report] Université côte d'azur. 2020. ⟨hal-02554102⟩

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