A 1-2-3-4 result for the 1-2-3 Conjecture in 5-regular graphs

Julien Bensmail 1
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : The 1-2-3 Conjecture, posed by Karoński, Łuczak and Thomason, asks whether every connected graph G different from K2 can be 3-edge-weighted so that every two adjacent vertices of G get distinct sums of incident weights. Towards that conjecture, the best-known result to date is due to Kalkowski, Karoński and Pfender, who proved that it holds when relaxed to 5-edge-weightings. Their proof builds upon a weighting algorithm designed by Kalkowski for a total version of the problem. In this work, we present new mechanisms for using Kalkowski's algorithm in the context of the 1-2-3 Conjecture. As a main result we prove that every 5-regular graph admits a 4-edge-weighting that permits to distinguish its adjacent vertices via their incident sums.
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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01509365
Contributeur : Julien Bensmail <>
Soumis le : lundi 17 avril 2017 - 11:57:04
Dernière modification le : jeudi 20 avril 2017 - 01:09:46

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Julien Bensmail. A 1-2-3-4 result for the 1-2-3 Conjecture in 5-regular graphs. 2017. <hal-01509365>

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