On the number of maximal independent sets in complete q-ary trees
-
Dmitriy S. Taletskiy
Abstract
The paper is concerned with the asymptotic behaviour of the number mi(Tq,n) of maximal independent sets in a complete q-ary tree of height n. For some constants α2 and β2 the asymptotic formula mi(T2,n)∼ α2⋅ (β2)2n is shown to hold as n → ∞. It is also proved that
Originally published in Diskretnaya Matematika (2016) 28, №4, 139–149 (in Russian).
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 16-31-60008-mol_a_dk
Funding statement: This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-31-60008-mol_a_dk) and the Laboratory of algorithms and analysis of network structures at the National Research University “Higher School of Economics”, Nizhny Novgorod Branch.
References
[1] Voronin V. P., Demakova E. V., “On the number of independent sets for some families of graphs”, Proc. IV Int. Conf. «Discrete models in control systems theory», Izd-vo MAKSPress, Moscow, 2000, 145–149 (in Russian).Search in Google Scholar
[2] Daynyak A. B., “On the number of independent sets in complete q-ary trees”, Uchenye zapiski Kazanskogo gos. un-ta. Seriya Fiz.-matem. nauki, 151, Izd-vo Kazanskogo un-ta, Kazan, 2009, 59–64 (in Russian).Search in Google Scholar
[3] Korshunov A. D., Sapozhenko A. A., “On the number of binary codes with distance 2”, Problemy Kibernetiki, 40 (1993), 111–140 (in Russian).Search in Google Scholar
[4] Kalkin, N.J., Wilf, H.S., “The number of independent sets in a grid graph”, SIAM J. Discr. Math., 11:1 (1997), 54–60.10.1137/S089548019528993XSearch in Google Scholar
[5] Kirschenhofer, P., Prodinger, H., Tichy, R., “Fibonacci numbers of graphs: II”, The Fibonacci Quarterly, 21:3 (1983), 219–229.10.1080/00150517.1983.12429948Search in Google Scholar
© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Functional limit theorem for a stopped random walk attaining a high level
- Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells
- Lower bound for the complexity of five-valued polarized polynomials
- The minimum number of negations in circuits for systems of multi-valued functions
- Bounded prefix concatenation operation and finite bases with respect to the superposition
- On the number of maximal independent sets in complete q-ary trees
- Lower estimate for the cardinality of the domain of universal functions for the class of linear Boolean functions
- Limit theorems for the logarithm of the order of a random A-mapping
Articles in the same Issue
- Frontmatter
- Functional limit theorem for a stopped random walk attaining a high level
- Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells
- Lower bound for the complexity of five-valued polarized polynomials
- The minimum number of negations in circuits for systems of multi-valued functions
- Bounded prefix concatenation operation and finite bases with respect to the superposition
- On the number of maximal independent sets in complete q-ary trees
- Lower estimate for the cardinality of the domain of universal functions for the class of linear Boolean functions
- Limit theorems for the logarithm of the order of a random A-mapping
