### Dominating Functions and Graphs

by Diestel and Shelah and Steprans. [DShS:443]

J London Math Soc, 1994

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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