# Sh:443

- Diestel, R., Shelah, S., & Steprāns, J. (1994).
*Dominating functions and graphs*. J. London Math. Soc. (2),**49**(1), 16–24. arXiv: math/9308215 DOI: 10.1112/jlms/49.1.16 MR: 1253008 -
Abstract:

A graph is called dominating if its vertices can be labelled with integers in such a way that for every function f:\omega\to\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. - published version (9p)

Bib entry

@article{Sh:443, author = {Diestel, Reinhard and Shelah, Saharon and Stepr{\={a}}ns, Juris}, title = {{Dominating functions and graphs}}, journal = {J. London Math. Soc. (2)}, fjournal = {Journal of the London Mathematical Society. Second Series}, volume = {49}, number = {1}, year = {1994}, pages = {16--24}, issn = {0024-6107}, mrnumber = {1253008}, mrclass = {05C78 (04A20)}, doi = {10.1112/jlms/49.1.16}, note = {\href{https://arxiv.org/abs/math/9308215}{arXiv: math/9308215}}, arxiv_number = {math/9308215} }