Abstract
We consider the largest number of minimal separators a graph on n vertices can have.-We give a new proof that this number is in O ((1+ √ 5/ 2)n n) We prove that this number is in ω (1.4457n), improving on the previous best lower bound of Ω(3n/3) ⊆ ω(1.4422n). This gives also an improved lower bound on the number of potential maximal cliques in a graph. We would like to emphasize that our proofs are short, simple, and elementary.
Cite
CITATION STYLE
Gaspers, S., & Mackenzie, S. (2016). On the number of minimal separators in graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9224 LNCS, pp. 116–121). Springer Verlag. https://doi.org/10.1007/978-3-662-53174-7_9
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