/Exposé /Talk/

The irregularity strength s(G) of a graph G is the smallest k such that the edges of G can be labelled with 1,...,k so that no two vertices are incident to the same sum of labels. This parameter was introduced in the late 1980s as an alternative way to deal with an optimisation problem where one aims at making a graph irregular by multiplying its edges in an optimal way. Since then, the irregularity strength has received a lot of attention, focusing mainly on proving bounds and investigating side aspects and variants.

In a recent work, we considered the algorithmic complexity of determining the irregularity strength of a given graph. We proved that two close variants of this problem are NP-hard, which we suspect might indicate that the original problem is hard too. Namely, we proved that determining the distant irregularity strength, where only vertices within a certain distance are required to be incident to different sums of labels, and the multiset irregularity strength, where any two distinct vertices are required to be incident to different multisets of labels, are NP-hard problems.

The talk will essentially be focused on introducing the general problem (which remains open to date), on going through most of the ideas behind the proofs of our two results, and on explaining what we can get and learn from our arguments and tools.

[Julien Bensmail] (Université Côte d'Azur )
http://jbensmai.fr/

Remarks / Remarques

Find all the information of the working group on this [ https://graphesetoptimisation.labri.fr/pmwiki.php/Groupe/GT?userlang=en | web page ] .
Retrouvez toutes les informations du GT sur cette [ https://graphesetoptimisation.labri.fr/pmwiki.php/Groupe/GT | page web ] .