A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from G̅ to G results in a copy of H. The minimum size of an H-saturated graph on n vertices is denoted sat(n,H), while the maximum size is the well studied extremal number, ex(n,H). The saturation spectrum for a graph H is the set of sizes of H saturated graphs between sat(n,H) and ex(n,H). In this paper we completely determine the saturation spectrum of stars and we show the saturation spectrum of paths is continuous from sat(n, Pk) to within a constant of ex(n, Pk) when n is sufficiently large.
@article{bwmeta1.element.doi-10_7151_dmgt_1954,
author = {Jill Faudree and Ralph J. Faudree and Ronald J. Gould and Michael S. Jacobson and Brent J. Thomas},
title = {Saturation Spectrum of Paths and Stars},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {811-822},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1954}
}
Jill Faudree; Ralph J. Faudree; Ronald J. Gould; Michael S. Jacobson; Brent J. Thomas. Saturation Spectrum of Paths and Stars. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 811-822. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1954/