# Edge partitions of the Rado graph

@article{Pouzet1996EdgePO, title={Edge partitions of the Rado graph}, author={Maurice Pouzet and Norbert Sauer}, journal={Combinatorica}, year={1996}, volume={16}, pages={505-520} }

We will prove that for every colouring of the edges of the Rado graph,ℛ (that is the countable homogeneous graph), with finitely many coulours, it contains an isomorphic copy whose edges are coloured with at most two of the colours. It was known [4] that there need not be a copy whose edges are coloured with only one of the colours. For the proof we use the lexicographical order on the vertices of the Rado graph, defined by Erdös, Hajnal and Pósa.Using the result we are able to describe a…

## 20 Citations

### COLORING SUBGRAPHS OF THE RADO GRAPH

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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.

### A Polychromatic Ramsey Theory for Ordinals

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### Another Look at the Erdős–Hajnal–Pósa Results on Partitioning Edges of the Rado Graph

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Erdős, Hajnal and Pósa exhibited a partition of the edges of the Rado graph which is a counterexample to and obtained that if every vertex of a graph has either in or in the complement of finite degree then .

### A List of Problems on the Reverse Mathematics of Ramsey Theory on the Rado Graph and on Infinite, Finitely Branching Trees

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This article discusses some recent trends in Ramsey theory on infinite structures. Trees and their Ramsey theory have been vital to these investigations. The main ideas behind the author's recent…

### Borel sets of Rado graphs and Ramsey's Theorem

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The well-known Galvin-Prikry Theorem states that Borel subsets of the Baire space are Ramsey: Given any Borel subset $\mathcal{X}\subseteq [\omega]^{\omega}$, where $[\omega]^{\omega}$ is endowed…

### The Ramsey Theory of Henson graphs

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For $k\ge 3$, the Henson graph $\mathcal{H}_k$ is the analogue of the Rado graph in which $k$-cliques are forbidden. Building on the author's result for $\mathcal{H}_3$, we prove that for each $k\ge…

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