论文标题
有限规则的顶点色图的分类
Classification of Finite Highly Regular Vertex-Coloured Graphs
论文作者
论文摘要
如果两个诱导的序列中的每个同构在k中，则颜色的图是k-紫tra词。如果最多k的一个顺序中的每个顶点的顶点数仅取决于S. 我们将有限的顶点色的k-紫质图和有限的顶点色的l-tuple常规图分别为k至少4和l至少5个。我们的定理尤其是有限的顶点色的超双重图，在该图中，超均匀的图表示该图同时在所有k中同时进行k-紫trahomosiens。
A coloured graph is k-ultrahomogeneous if every isomorphism between two induced subgraphs of order at most k extends to an automorphism. A coloured graph is t-tuple regular if the number of vertices adjacent to every vertex in a set S of order at most k depends only on the isomorphism type of the subgraph induced by S. We classify the finite vertex-coloured k-ultrahomogeneous graphs and the finite vertex-coloured l-tuple regular graphs for k at least 4 and l at least 5, respectively. Our theorem in particular classifies finite vertex-coloured ultrahomogeneous graphs, where ultrahomogeneous means the graph is simultaneously k-ultrahomogeneous for all k.
