Countable splitting graphs

Volume 212 / 2011

Nick Haverkamp Fundamenta Mathematicae 212 (2011), 217-233 MSC: 03E17, 05C75, 05C99. DOI: 10.4064/fm212-3-2


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.


  • Nick HaverkampInstitut für Philosophie
    Humboldt Universität
    Unter den Linden 6
    10099 Berlin, Germany

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