A Survey of Minimum Saturated Graphs

@article{Faudree2011ASO,
  title={A Survey of Minimum Saturated Graphs},
  author={J. Faudree and R. Faudree and J. R. Schmitt},
  journal={Electronic Journal of Combinatorics},
  year={2011},
  volume={1000}
}
Given a family of (hyper)graphs $\mathcal{F}$ a (hyper)graph $G$ is said to be $\mathcal{F}$-saturated if $G$ is $F$-free for any $F \in\mathcal{F}$ but for any edge e in the complement of $G$ the (hyper)graph $G + e$ contains some $F\in\mathcal{F}$. We survey the problem of determining the minimum size of an $\mathcal{F}$-saturated (hyper)graph and collect many open problems and conjectures. 
102 Citations
Star saturation number of random graphs
  • 1
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Hypergraph Saturation Irregularities
  • 1
  • PDF
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  • 10
  • PDF
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  • 1
  • PDF
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The Game Saturation Number of a Graph
  • 9
  • PDF
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  • 3
  • PDF
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2
3
4
5
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References

SHOWING 1-10 OF 157 REFERENCES
Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size
  • 20
  • PDF
Saturation Numbers for Trees
  • 15
  • PDF
On Minimum Saturated Matrices
  • 4
  • PDF
Saturation Numbers of Books
  • 21
  • PDF
A General Lower Bound for Potentially H-Graphic Sequences
  • 7
  • PDF
Lower Bound for the Size of Maximal Nontraceable Graphs
  • 11
  • PDF
Minimum degree and the minimum size of K22-saturated graphs
  • 6
  • PDF
Saturated graphs with minimal number of edges
  • 124
Asymptotic results on saturated graphs
  • 11
...
1
2
3
4
5
...