Gaps in the Saturation Spectrum of Trees

Authors

Ronald J. Gould, Emory UniversityFollow
Paul Horn, University of DenverFollow
Michael S. Jacobson, University of Colorado DenverFollow
Brent J. Thomas, Utah State UniversityFollow

Document Type

Article

Journal/Book Title/Conference

Discussiones Mathematicae Graph Theory

Volume

39

Issue

1

Publisher

University of Zielona Góra

Publication Date

5-17-2018

First Page

157

Last Page

170

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Abstract

A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from the complement of G to G results in a copy of H. The minimum number of edges (the 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 show that paths, trees with a vertex adjacent to many leaves, and brooms have a gap in the saturation spectrum.

Recommended Citation

Gould, Ronald J., Horn, Paul, Jacobson, Michael S., and Thomas, Brent J. "Gaps in the Saturation Spectrum of Trees." Discussiones Mathematicae Graph Theory, vol. 39, 2018, pp. 157-170. https://doi.org/10.7151/dmgt.2073