图的染色是图论研究的重要内容，在实际问题中有广泛应用。本项目从图的结构性质入手，研究图的邻点区别边染色和全染色、邻和区别边染色和全染色、距离2点区别边染色和全染色等问题。围绕着本领域的几个公开问题，借助组合、代数、概率、权转移、边分解、算法分析等方法，对上述参数进行刻画或给出好的上界。在图的邻点区别边染色方面，证明每个正常图的点区别边色数至多是2Δ，及Δ≥13的平面图有邻点区别边色数Δ+1当且仅当它有两个相邻的最大度点；在图的邻点区别全染色方面，证明每个图的邻点区别全色数至多是⌈3Δ/2⌉，及Δ≥11的平面图有邻点区别全色数Δ+2当且仅当它有两个相邻的最大度点；在图的距离2点区别边染色方面，证明存在一个常数c使得每个图的距离2点区别边色数至多是cΔ。拟在四年内完成学术论文20余篇，其中10篇以上发表在SCI杂志上。

Graph coloring is an important branch of graph theory, which has wide applications in practical problems. In this project, starting with the structural properties of graphs, we discuss the adjacent vertex-distinguishing edge (total) coloring, the adjacent sum-distinguishing edge (total) coloring, and the distance 2 vertex-distinguishing edge (total) coloring. The research aims at several open problems in related areas and makes use of combinatorial, algebraic, probabilistic, discharging and edge-partition methods. We try to show the following results: (1) The adjacent vertex-distinguishing chromatic index of a normal graph is at most 2Δ, and a planar graph with Δ≥13 has the adjacent vertex-distinguishing chromatic index Δ+1 if and only if it contains adjacent Δ-vertices. (2) The adjacent vertex-distinguishing total chromatic number of a graph is at most ⌈3Δ/2⌉, and a planar graph with Δ≥11 has the adjacent vertex-distinguishing total chromatic number Δ+2 if and only if it contains adjacent Δ-vertices. (3) There exists a constant c such that the distance 2 vertex-distinguishing chromatic index of every graph is bounded by cΔ. At least 20 papers are published after the project is finished, at least 10 of which are indexed by SCI.