A limit theorem for the Shannon capacities of odd cycles I

Author:
Tom Bohman

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3559-3569

MSC (2000):
Primary 94A15, 05C35, 05C38

Published electronically:
June 5, 2003

MathSciNet review:
1991769

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 .

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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:
http://dx.doi.org/10.1090/S0002-9939-03-06495-5

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

Published electronically:
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 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 A limit theorem for the Shannon capacities of odd cycles II

Communicated by:
John R. Stembridge

Article copyright:
© Copyright 2003
American Mathematical Society