Countable splitting graphs

@article{Haverkamp2011CountableSG,
  title={Countable splitting graphs},
  author={Nick Haverkamp},
  journal={Fundamenta Mathematicae},
  year={2011},
  volume={212},
  pages={217-233}
}
  • N. Haverkamp
  • Published 2011
  • Mathematics
  • Fundamenta Mathematicae
A graph is called splitting if there is a 0-1 labelling of its vertices such that for every infinite set C of natural numbers there is a sequence of labels along a 1-way infinite path in the graph whose restriction to C is not eventually constant. We characterize the countable splitting graphs as those containing a subgraph of one of three simple types. 

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