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Saturation Spectrum of Paths and Stars

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Faudree J., Faudree R. J., Gould R. J., Jacobson M. S., Thomas B. J.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 3

811-822

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Faudree J.

1 Faudree R. J.

1 Gould R. J.

1 Jacobson M. S.

1 Thomas B. J.

1 2017

Wyniki wyszukiwania

Saturation Spectrum of Paths and Stars