报告题目：The 1-2 conjecture and progress on the (2,2)-choosability conjecture

报告人：邓科财副教授，华侨大学

报告时间：2025年10月25日（周六）10:00-11:00

报告地点：20-306

报告摘要：For a simple graph $G=(V,E)$, a \emph{proper total weighting} is a mapping  $w: V\cup E\rightarrow \mathbb R$ such that adjacent vertices have distinct weighted degrees. The graph $G$ is said \emph{$(2,2)$-choosable} if, for any list assignment  $L$ that assigns to each $z$ in $V\cup E$ a set $L(z)$ of two real numbers, there exists a proper total weighting $w$ with $w(z)\in L(z)$ for every $z\in V\cup E$. Wong and Zhu conjectured that every simple graph is $(2,2)$-choosable. This conjecture remains open.

For a set $\{a,b\}\subset \mathbb R$, its span is defined as $|b-a|$. We call a graph $G=(V,E)$ \emph{uniform-span $(2,2)$-choosable} if, for any list assignment $L$ that assigns to every $z \in V\cup E$ a two-element list of a common span, there exists a proper total weighting respecting to the assignment. We show that every graph is uniform-span $(2,2)$-choosable. This confirms the 1-2 conjecture in full generality, and offers supporting evidence to the (2, 2)-choosability conjecture.

报告人简介：邓科财，厦门大学数学科学学院本科、硕士、博士毕业，师从钱建国教授。现任华侨大学数学科学学院副教授、硕士生导师。主要研究方向为图的染色、计数、极值问题等，已发表学术论文24篇，包括《J. Comb. Theory, Ser. B》、《Discrete Math.》、《J. Stat. Mech. Theory Exp.》等期刊。主持国家自然科学基金青年项目，福建省自然科学基金，中央高校基本科研业务费各1项。担任福建省运筹学会理事。

邀请人：朱绪鼎