Discrete Applied Math Seminar by Xuding Zhu: List version of 1-2-3 conjecture

Speaker: Xuding Zhu, Zhejiang Normal University

Title: List version of 1-2-3 conjecture

Abstract:  The well-known 1-2-3 Conjecture by Karonski, Luczak 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, and sketch the proof of a recent result that the conclusion would be true if each edge has 5 choices.

Please contact Organizers for Zoom meeting info.

Seminar Contacts: Hemanshu Kaul (kaul@iit.edu) and Samantha Dahlberg (sdahlberg@iit.edu)