- Title: A contribution to distinguishing labellings of graphs
- When: December 15, 2020 — 09:00
- Where: online with live streaming on Youtube
- Committee:
- Cristina Bazgan, PR, Université Paris-Dauphine, Paris
- Frédéric Cazals, DR, Inria Sophia Antipolis – Méditerranée
- Louis Esperet CR HDR, CNRS, G-SCOP, Grenoble
- Mickaël Montassier (referee), PR, Université de Montpellier
- Éric Sopena PR, Université de Bordeaux
- Stéphan Thomassé, PR, ENS de Lyon
- Olivier Togni (referee), PR, Université de Bourgogne, Dijon
- Xuding Zhu (referee), PR, National Sun Yat-sen University (Taïwan)
- Manuscript: http://jbensmai.fr/hdr/
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Abstract: During the talk, I will present some of my contribution to distinguishing labellings of graphs, and the so-called 1-2-3 Conjecture that occupies an important place in this field. The general objective in this kind of problems is, given a (connected undirected) graph, to weight its edges in such a way that the adjacent vertices get distinguishable accordingly to some parameter computed from the edge-weighting. For instance, in the 1-2-3 Conjecture, raised by Karonski, Łuczak and Thomason in 2004, the aim is to weight the edges with 1,2,3 so that adjacent vertices get distinguished accordingly to their sums of incident weights.
Although the 1-2-3 Conjecture was raised as nothing but a toy problem when it was introduced, several results in the recent years have established its deeper nature. The conjecture, by its very definition, has undoubtedly an algebraic nature. Some results have also established that it has some decompositional flavour. Although the conjecture is rather artificial, it is also related to other classical notions of graph theory, such as proper vertex-colourings of graphs.
Through the results I will focus on during the talk, my main goal is to point out how deep this field is, and the many aspects of interest that are worth considering.
