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# Xuding Zhu (朱緒鼎), List version of 1-2-3 conjecture

## July 10 Monday @ 4:30 PM - 5:30 PM KST

Room B109,
IBS (기초과학연구원)

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.