Combinatorics Colloquium by Prof. Xuding Zhu (Zhejiang Normal University, Jinhua, China)
Abstract:
The well-known 1-2-3 Conjecture by Karo\'{n}ski, {\L}uczak, 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 more generally 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.
