Saturation Spectrum of Paths and Stars

Jill Faudree, et al. "Saturation Spectrum of Paths and Stars." Discussiones Mathematicae Graph Theory 37.3 (2017): 811-822. <http://eudml.org/doc/288512>.

@article{JillFaudree2017,
abstract = {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.},
author = {Jill Faudree, Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson, Brent J. Thomas},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {saturation spectrum; stars; paths},
language = {eng},
number = {3},
pages = {811-822},
title = {Saturation Spectrum of Paths and Stars},
url = {http://eudml.org/doc/288512},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Jill Faudree
AU - Ralph J. Faudree
AU - Ronald J. Gould
AU - Michael S. Jacobson
AU - Brent J. Thomas
TI - Saturation Spectrum of Paths and Stars
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 3
SP - 811
EP - 822
AB - 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.
LA - eng
KW - saturation spectrum; stars; paths
UR - http://eudml.org/doc/288512
ER -