# Sh:443

• Diestel, R., Shelah, S., & Steprāns, J. (1994). Dominating functions and graphs. J. London Math. Soc. (2), 49(1), 16–24.
• 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}
}