# Saturation Spectrum of Paths and Stars

Jill Faudree; Ralph J. Faudree; Ronald J. Gould; Michael S. Jacobson; Brent J. Thomas

Discussiones Mathematicae Graph Theory (2017)

- Volume: 37, Issue: 3, page 811-822
- ISSN: 2083-5892

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topJill 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 -