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Another look at the Erdős-Hajnal-Pósa results on partitioning edges and the Rado graph. (English summary) Paul Erdős and his mathematics (Budapest, 1999). Combinatorica 21 (2001), no. 2, 293–308. The Rado graph R is the unique countable graph with the property that for every finite graph G and any vertex a of G, each embedding of G − a into R can be extended to an embedding of G into R. If G1,..., Gn are some graphs, then R ↣ (G1,..., Gn) e means that for every partition A1,..., An of the set of edges of the Rado graph R, for some i there is an embedding of Gi into R such that all edges of the embedded graph belong to the set Ai

Year: 2011

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