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

Dedicated to the memory of Paul Erdős

Erdős, Hajnal and Pósa exhibited in [1] a partition (U,D) of the edges of the Rado graph which is a counterexample to . They also obtained that if every vertex of a graph has either in or in the complement of finite degree then .

We will characterize all graphs so that .

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Received October 29, 1999

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ID="†" Supported by NSERC of Canada Grant #691325.

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Sauer, N. Another Look at the Erdős–Hajnal–Pósa Results on Partitioning Edges of the Rado Graph. Combinatorica 21, 293–308 (2001). https://doi.org/10.1007/s004930100026

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  • AMS Subject Classification (2000) Classes:  03E02, 05C55, 03C10