Discussiones Mathematicae Graph Theory (Aug 2017)

Saturation Spectrum of Paths and Stars

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

DOI
https://doi.org/10.7151/dmgt.1954
Journal volume & issue
Vol. 37, no. 3
pp. 811 – 822

Abstract

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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.

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