标题： 树分解的小图以及将它们作为实代数函数的Reeb图实现的图 显示英文标题

标题： Graphs with tree decompositions of small graphs and realizing them as the Reeb graphs of real algebraic functions

摘要： 我们一直对图以及将它们作为显式实代数函数的Reeb图感兴趣。 可微函数的Reeb图是定义域流形的商空间，被看作由所有单点的原像的所有成分组成的空间。 自20世纪上半叶Morse函数理论诞生以来，Reeb图一直是流形几何中的基本且强有力的工具。 我们可以很容易地看出，维度至少为$2$的单位球面的自然高度的Reeb图是一个恰好有一个边和两个边的图。 我们关注的是分解成树状结构良好的图的实现，每个顶点对应一个恰好有一个边和两个边的图或者一个恰好有两个边且与圆同胚的图。 显示英文摘要

摘要： We have been interested in graphs and realizing them as Reeb graphs of explicit real algebraic functions. The Reeb graph of a differentiable function is the quotient space of the manifold of the domain, regarded as the space consisting of all components of preimages of all single points. Reeb graphs have been fundamental and strong tools in geometry of manifolds since the birth of theory of Morse functions, in the former half of the 20th century. We can easily see that the Reeb graph of the natural height of the unit sphere whose dimension is at least $2$ is a graph with exactly one edge and two edges. We are concerned with realizations of graphs decomposed into trees nicely, each vertex of which corresponds to a graph with exactly one edge and two edges or a graph with exactly two edges homeomorphic to a circle.