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- W2279593527 abstract "A set of vertices in a graph is connected if the set induces a connected subgraph. Using Shearer’s entropy lemma, we show that the number of connected sets in an (n)-vertex graph with maximum vertex degree (d) is (O(1.9351^n)) for (d=3), (O(1.9812^n)) for (d=4), and (O(1.9940^n)) for (d=5). Dually, we construct infinite families of generalized ladder graphs whose number of connected sets is bounded from below by (varOmega (1.5537^n)) for (d=3), (varOmega (1.6180^n)) for (d=4), and (varOmega (1.7320^n)) for (d=5)." @default.
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- W2279593527 date "2014-01-01" @default.
- W2279593527 modified "2023-09-24" @default.
- W2279593527 title "On the Number of Connected Sets in Bounded Degree Graphs" @default.
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- W2279593527 doi "https://doi.org/10.1007/978-3-319-12340-0_28" @default.
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