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.

翻译：关系结构R被称为超齐次的，若R的任意有限导出子结构间的同构均可延拓为R的自同构。本文对含有一个非对称二元关系及任意多个一元关系的有限二元关系结构进行了超齐次性分类。换言之，我们分类了有限顶点着色超齐次有向图。该分类包含若干通用方法，通过这些方法可将有向图进行组合或扩展以构造新的超齐次图。结合显式给出的特例，我们由此精确获得了所有顶点着色超齐次有向图。我们的核心技术是一种数学工具，它能精确刻画在何种条件下，两个具有互不相交一元关系的二元关系结构可以组合形成更大的超齐次结构。