Dominating functions and graphs
Reinhard Diestel, Saharon Shelah, Juris Steprāns
Abstract
A graph is called dominating if its vertices can be labelled with integers in such a way that for every function f: omega-> omega the graph contains a ray whose sequence of labels eventually exceeds f. We obtain a characterization of these graphs by producing a small family of dominating graphs with the property that every dominating graph must contain some member of the family.
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