图着色下的树顶点邻集的行为

摘要

图着色下的树顶点邻集的行为展示了有趣的问题.该文证明了树顶点邻集的行为对一些图全着色有着非常强的性质,或多或少地揭示了树顶点邻集的行为与着色猜想的一些关系.作者期望应用这种邻集的行为去深刻地研究图着色问题.%Behaviors of vertex neighbors of trees under certain graph colorings show some interesting problems. These behaviors of vertex neighbors of trees give stronger properties for known total colorings, and reveal some relations between the coloring conjectures, more or less.It is hoped to apply these behaviors to study deeply graph coloring problems.