Abstract

The well-known 1-2-3 Conjecture by Karoński Łuczak and Thomason states that the edges of any connected graph with at least three vertices can be assigned weights 1, 2 or 3 so that for each edge uv the sums of the weights at u and at v are distinct. The list version of the 1-2-3 Conjecture by Bartnicki, Grytczuk and Niwczyk states that the same holds if each edge e has the choice of weights not necessarily from {1, 2, 3}, but from any set {x(e), y(e), z(e)} of three real numbers. The goal of this talk is to survey developments on the 1-2-3 Conjecture, especially on the list version of the 1-2-3 Conjecture.