Saturation Spectrum of Paths and Stars
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...
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| Format: | Article |
| Language: | English |
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Sciendo
2017-08-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.1954 |
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doaj-a54c4c29733b4989bb0a016fe2e69b4f2021-09-05T17:20:22ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922017-08-0137381182210.7151/dmgt.1954dmgt.1954Saturation Spectrum of Paths and StarsFaudree Jill0Faudree Ralph J.1Gould Ronald J.2Jacobson Michael S.3Thomas Brent J.4Department of Mathematics and Statistics, University of Alaska FairbanksDepartment of Mathematical Sciences, University of MemphisDepartment of Mathematics and Computer Science, Emory UniversityDepartment of Mathematics and Statistical Sciences, University of Colorado DenverDepartment of Mathematics and Statistical Sciences, University of Colorado DenverA 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.https://doi.org/10.7151/dmgt.1954saturation spectrumstarspaths05c3505c05 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Faudree Jill Faudree Ralph J. Gould Ronald J. Jacobson Michael S. Thomas Brent J. |
| spellingShingle |
Faudree Jill Faudree Ralph J. Gould Ronald J. Jacobson Michael S. Thomas Brent J. Saturation Spectrum of Paths and Stars Discussiones Mathematicae Graph Theory saturation spectrum stars paths 05c35 05c05 |
| author_facet |
Faudree Jill Faudree Ralph J. Gould Ronald J. Jacobson Michael S. Thomas Brent J. |
| author_sort |
Faudree Jill |
| title |
Saturation Spectrum of Paths and Stars |
| title_short |
Saturation Spectrum of Paths and Stars |
| title_full |
Saturation Spectrum of Paths and Stars |
| title_fullStr |
Saturation Spectrum of Paths and Stars |
| title_full_unstemmed |
Saturation Spectrum of Paths and Stars |
| title_sort |
saturation spectrum of paths and stars |
| publisher |
Sciendo |
| series |
Discussiones Mathematicae Graph Theory |
| issn |
2083-5892 |
| publishDate |
2017-08-01 |
| description |
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. |
| topic |
saturation spectrum stars paths 05c35 05c05 |
| url |
https://doi.org/10.7151/dmgt.1954 |
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AT faudreejill saturationspectrumofpathsandstars AT faudreeralphj saturationspectrumofpathsandstars AT gouldronaldj saturationspectrumofpathsandstars AT jacobsonmichaels saturationspectrumofpathsandstars AT thomasbrentj saturationspectrumofpathsandstars |
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1717786461989765120 |