有限顶点着色的超齐原有向图
Finite Vertex-colored Ultrahomogeneous Oriented Graphs
AI总结：
本研究对含一个非对称二元关系、任意多个一元关系的有限超齐次二元关系结构（即有限顶点着色超齐原有向图）完成分类，提出构造新超齐次图的通用方法与组合判定工具，结合例外情形得到全部此类图。
摘要：
若关系结构R的每个有限诱导子结构同构都能扩展为R的自同构，则称R是超齐次的。我们对含一个非对称二元关系和任意多个一元关系的超齐次有限二元关系结构进行了分类，换言之，完成了有限顶点着色超齐原有向图的分类。该分类包含若干通用方法，可通过组合或扩展有向图构造新的超齐次图，结合明确给出的例外情形，我们以此得到了全部顶点着色超齐原有向图。我们的核心技术是一种工具，可精确刻画两个一元关系不相交的二元关系结构可组合为更大超齐次结构的条件。
英文摘要：
A relational structure R is ultrahomogeneous if every isomorphism of finite induced substructures of R extends to an automorphism of R. We classify the ultrahomogeneous finite binary relational structures with one asymmetric binary relation and arbitrarily many unary relations. In other words, we classify the finite vertex-colored oriented ultrahomogeneous graphs. The classification comprises several general methods with which directed graphs can be combined or extended to create new ultrahomogeneous graphs. Together with explicitly given exceptions, we obtain exactly all vertex-colored oriented ultrahomogeneous graphs this way. Our main technique is a technical tool that characterizes precisely under which conditions two binary relational structures with disjoint unary relations can be combined to form a larger ultrahomogeneous structure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
