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

講座時(shí)間：2019-09-11 14:30:00

講座地點(diǎn)：南校區(qū)信遠(yuǎn)樓II-206

講座人：Julien BENSMAIL

講座人介紹：

自2016年起Julien Bensmail是法國(guó)尼斯大學(xué)副教授，也是I3S/法國(guó)信息與自動(dòng)化研究所項(xiàng)目組COATI的成員。在 Olivier Baudon教授和 éric Sopena教授的指導(dǎo)下，于2014年獲得波爾多大學(xué)博士學(xué)位。在尼斯工作之前，做了兩個(gè)為期一年的博士后，一個(gè)是于2014-2015期間在里昂，合作導(dǎo)師是Stéphan Thomassé教授；另一個(gè)是于2015-2016期間在哥本哈根，合作導(dǎo)師是Carsten Thomassen教授。他的主要研究興趣包括染色、分解、劃分等圖論問(wèn)題，特別是這些問(wèn)題的組合性質(zhì)與算法方面的研究。他的研究成果涉及到圖論里的一些問(wèn)題和概念，包括著名的任意可劃分圖類、圖的強(qiáng)染色數(shù)、Barát-Thomassen猜想和1-2-3猜想。

講座內(nèi)容：

The 1-2-3 Conjecture, posed in 2004 by Karoński, ?uczak 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.

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院