Analysis of the impact of the number of edges in connected graphs on the computational complexity of the independent set problem
β Scribed by D. S. Malyshev
- Book ID
- 114994297
- Publisher
- Pleiades Publishing
- Year
- 2012
- Tongue
- English
- Weight
- 473 KB
- Volume
- 6
- Category
- Article
- ISSN
- 1990-4789
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π SIMILAR VOLUMES
Generalizing a theorem of Moon and Moser. we determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50. = I .32. . .). Example 1.2. Let b, = i(C,), where C,z denotes the circuit of length n. Then b, = 3, 6, = 2, b, = 5, and b,
a b s t r a c t Assume that n and Ξ΄ are positive integers with 3 β€ Ξ΄ < n. Let hc(n, Ξ΄) be the minimum number of edges required to guarantee an n-vertex graph G with minimum degree Ξ΄(G) β₯ Ξ΄ to be hamiltonian connected.
We determine the maximum on n vertices can have, and we a question of Wilf. number of maximal independent sets which a connected graph completely characterize the extremal graphs, thereby answering \* Partially supported by NSF grant number DIMS-8401281. t Partially supported by NSF grant number D S