图的反魔幻标号和列表1-2-3猜想

图的染色和标号问题蕴含着丰富的内容，其中以四色猜想为中心的点可区别染色和标号为研究重点。本课题主要研究与图的非正则强度相关的经典染色和标号问题，具体包括：图的反魔幻标号猜想和列表1-2-3猜想及相关问题等。我们将利用边分解及组合知识进一步完善图与有向图的反魔幻标号的相关结果；结合代数方法（组合零点定理和矩阵的permanent理论），经典的充放电技术等研究方法来研究列表1-2-3猜想和邻和可区别染色问题，力求解决几个困难问题，在此方向上有质的提高。本课题的研究涉及到图与有向图的结构，组合理论，图的染色等多个领域，对图论的理论发展和创新都有非常重要的研究意义。

There contains a wealth of content in the problem of coloring and labeling of graphs. The research focuses on that, vertex distinguishing coloring and labeling centered on Four-color Conjecture. The main researching area of this project is several classical problems of coloring and labeling related to irregularity strength of graphs, including Antimagic Labeling Conjecture， List 1-2-3 Conjecture and so forth. We will further improve the relevant results of antimagic labeling of graphs and digraphs by the method of edge decomposation and combinatorial theory; Besides, by combining Algebraic Method (specifically, Combinatorial Nullstellensatz Theorem and permanent theory of matrix) with discharging method, we will study list 1-2-3 conjecture and neighbor sum (set) distinguishing coloring problems, trying to figure out several difficult problems and achieving qualitative improvement in the research of this field. This project involves many fields including the structure of graphs, combinatorial theory and graph coloring problems. It is of great significance for the theoretical development and innovation of graph theory.