Rainbow Saturation
Abstract
We introduce a notion of rainbow saturation and the corresponding rainbow saturation number. This is the saturation version of the rainbow Tur\'an numbers whose systematic study was initiated by Keevash, Mubayi, Sudakov, and Verstra\"ete. We give examples of graphs for which the rainbow saturation number is bounded away from the ordinary saturation number. This includes all complete graphs for , and several bipartite graphs. It is notable that there are non-bipartite graphs for which this is the case, as this does not happen when it comes to the rainbow extremal number versus the traditional extremal number. We also show that saturation numbers are linear for a large class of graphs, providing a partial rainbow analogue of a well known theorem of K\'asonyi and Tuza. We conclude this paper with related open questions and conjectures.
Cite
@article{arxiv.2003.13200,
title = {Rainbow Saturation},
author = {Neal Bushaw and Daniel Johnston and Puck Rombach},
journal= {arXiv preprint arXiv:2003.13200},
year = {2022}
}