On the "Quest" towards a Directed Variant of the 1-2-3 Conjecture

讲座名称：On the "Quest" towards a Directed Variant of the 1-2-3 Conjecture

讲座时间：2019-09-11 14:30:00

讲座地点：南校区信远楼II-206

讲座人：Julien BENSMAIL

讲座人介绍：

自2016年起Julien Bensmail是法国尼斯大学副教授，也是I3S/法国信息与自动化研究所项目组COATI的成员。在 Olivier Baudon教授和 Éric Sopena教授的指导下，于2014年获得波尔多大学博士学位。在尼斯工作之前，做了两个为期一年的博士后，一个是于2014-2015期间在里昂，合作导师是Stéphan Thomassé教授；另一个是于2015-2016期间在哥本哈根，合作导师是Carsten Thomassen教授。他的主要研究兴趣包括染色、分解、划分等图论问题，特别是这些问题的组合性质与算法方面的研究。他的研究成果涉及到图论里的一些问题和概念，包括著名的任意可划分图类、图的强染色数、Barát-Thomassen猜想和1-2-3猜想。

讲座内容：

The 1-2-3 Conjecture, posed in 2004 by Karoński, Łuczak and Thomason, asks whether the edges of every connected graph different from K2 can be weighted with weights 1,2,3 so that no two adjacent vertices are incident to the same sum of incident weights. Since its introduction, this conjecture has been attracting more and more attention. In particular, several works have been dedicated to verifying the 1-2-3 Conjecture for various classes of graphs, proving modified forms of the conjecture, and investigating several aspects such as algorithmic ones.

In graph theory, one legitimate direction for research regarding an undirected graph problem is to wonder about possible generalisations to digraphs. In the recent years, several attempts have been made for bringing the 1-2-3 Conjecture to digraphs. The goal of this talk will be to survey most of these attempts. In particular, we will stress out why things have been rather disappointing so far, and why the "quest" towards a directed 1-2-3 Conjecture might be not over yet.

主办单位：数学与统计学院