A limit theorem for the Shannon capacities of odd cycles. II
Author:
Tom Bohman
Journal:
Proc. Amer. Math. Soc. 133 (2005), 537543
MSC (2000):
Primary 94A15, 05C35, 05C38
Published electronically:
September 8, 2004
MathSciNet review:
2093078
Fulltext PDF Free Access
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Abstract: It follows from a construction for independent sets in the powers of odd cycles given in the predecessor of this paper that the limit as goes to infinity of is zero, where is the Shannon capacity of a graph . This paper contains a shorter proof of this limit theorem that is based on an `expansion process' introduced in an older paper of L. Baumert, R. McEliece, E. Rodemich, H. Rumsey, R. Stanley and H. Taylor. We also refute a conjecture from that paper, using ideas from the predecessor of this paper.
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Additional Information
Tom Bohman
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Email:
tbohman@moser.math.cmu.edu
DOI:
http://dx.doi.org/10.1090/S0002993904074702
PII:
S 00029939(04)074702
Keywords:
Shannon capacity,
odd cycles
Received by editor(s):
May 30, 2003
Received by editor(s) in revised form:
August 5, 2003
Published electronically:
September 8, 2004
Additional Notes:
This research was supported in part by NSF Grant DMS0100400.
Communicated by:
John R. Stembridge
Article copyright:
© Copyright 2004 American Mathematical Society
