Discussiones Mathematicae Graph Theory
University of Zielona Góra
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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 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.
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