Countable splitting graphs
@article{Haverkamp2011CountableSG,
title={Countable splitting graphs},
author={Nick Haverkamp},
journal={Fundamenta Mathematicae},
year={2011},
volume={212},
pages={217-233}
}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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