%0 Journal Article
%T Dominating functions and graphs
%A Reinhard Diestel
%A Saharon Shelah
%A Juris Stepr¨ˇns
%J Mathematics
%D 1993
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/9308215v1