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A limit theorem for the Shannon capacities of odd cycles I
Author(s):
Tom
Bohman
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3559-3569.
MSC (2000):
Primary 94A15, 05C35, 05C38
Posted:
June 5, 2003
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Abstract:
This paper contains a construction for independent sets in the powers of odd cycles. It follows from this construction that the limit as  goes to infinity of  is zero, where  is the Shannon capacity of the graph  .
References:
-
- 1.
- N. Alon, The Shannon capacity of a union, Combinatorica, 18 (1998), 301-310. MR 2000i:05096
- 2.
- L. Baumert, R. McEliece, E. Rodemich, H. Rumsey, R. Stanley, and H. Taylor, A Combinatorial Packing Problem, Computers in Algebra and Number Theory, American Mathematical Society, Providence, RI, 1971, pp. 97-108. MR 49:2437
- 3.
- C. Berge, Balanced hypergraphs and some applications to graph theory. A survey of combinatorial theory, North-Holland, Amsterdam and London, 1973. MR 51:2970
- 4.
- T. Bohman, M. Ruszinkó, and L. Thoma, Shannon capacity of large odd cycles, Proceedings of the 2000 IEEE International Symposium on Information Theory, June 25-30, Sorrento, Italy, p. 179.
- 5.
- W. Haemers, On some problems of Lovász concerning the Shannon capacity of a graph, IEEE Transactions on Information Theory, 25(2) (1979), 231-232. MR 80g:94040
- 6.
- W. Haemers, An upper bound for the Shannon capacity of a graph, Colloquia Mathematica Societatis János Bolyai, 25: Algebraic Methods in Graph Theory, Szeged (Hungary), 1978, 267-272. MR 83m:05098
- 7.
- R. S. Hales, Numerical invariants and the strong product of graphs, Journal of Combinatorial Theory - B, 15 (1973), 146-155. MR 48:177
- 8.
- J. Körner and A. Orlitsky, Zero-error information theory, IEEE Transactions on Information Theory 44(6) (1998), 2207-2229. MR 99h:94034
- 9.
- L. Lovász, On the Shannon capacity of a graph, IEEE Transactions on Information Theory 25(1) (1979), 1-7. MR 81g:05095
- 10.
- R. J. McEliece, E. R. Rodemich, and H. C. Rumsey, The Lovász bound and some generalizations, Journal of Combinatorics, Information and Systems Science 3 (1978), 134-152. MR 80a:05168
- 11.
- M. Rosenfeld, On a problem of C. E. Shannon in graph theory, Proceedings of the American Mathematical Society, 18 (1967), 315-319. MR 34:7405
- 12.
- C. E. Shannon, The zero-error capacity of a noisy channel, Institute of Radio Engineers Transactions on Information Theory, 2(3) (1956), 8-19. MR 19:623b
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Additional Information:
Tom
Bohman
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Address at time of publication:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Email:
tbohman@moser.math.cmu.edu
DOI:
10.1090/S0002-9939-03-06495-5
PII:
S 0002-9939(03)06495-5
Keywords:
Shannon capacity,
odd cycles
Received by editor(s):
May 17, 2000
Received by editor(s) in revised form:
June 21, 2000 and September 18, 2001
Posted:
June 5, 2003
Additional Notes:
This research was supported in part by NSF Grant DMS-9627408
While this paper was on its way to press, the author discovered {\em A combinatorial packing problem}, by L. Baumert et al., 1971, which contains an idea that yields an alternate (and shorter) proof of Theorem 1.1. The shorter proof together with some observations and questions that arise from comparing the two ideas are treated in the forth-coming manuscript {\em A limit theorem for the Shannon capacities of odd cycles II}
Communicated by:
John R. Stembridge
Copyright of article:
Copyright
2003,
American Mathematical Society
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