Coloring Subgraphs of the Rado Graph

Given a universal binary countable homogeneous structure U and n , there is a partition of the induced n-element substructures of U into finitely many classes so that for any partition C0, C1, . . . , Cm-1 of such a class Q into finitely many parts there is a number k m and a copy U of U in U so that all of the induced n-element substructures of U which are in Q are also in Ck. The partition of the induced n-element substructures of U is explicitly given and a somewhat sharper result as the one stated above is proven.

• Type: Journal
• Year: 2006
• Where: COMBINATORICA
• Authors: Norbert W. Sauer
• Keywords: COMBINATORICA 2006, Countable Homogeneous Structure, N-element Substructures, Universal Binary