On the bandwidth of 3-dimensional Hamming graphs

Authors:
J. Balogh;S. L. Bezrukov;L. H. Harper;A. Seress
Affiliations:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States;Department of Math and Comp. Sci., University of Wisconsin-Superior, Superior, WI 54880-4500, United States;Department of Mathematics, University of California, Riverside, CA 92521, United States;Department of Mathematics, Ohio State University, Columbus, OH 43210, United States
Venue:
Theoretical Computer Science
Year:
2008

Citing 3
Cited 1

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Computers and Intractability: A Guide to the Theory of NP-Completeness
On the bandwidth of a Hamming graph

Theoretical Computer Science
Note: On the variance of Shannon products of graphs

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Antibandwidth and cyclic antibandwidth of Hamming graphs

Discrete Applied Mathematics

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Abstract

This paper presents strategies for improving the known upper and lower bounds for the bandwidth of Hamming graphs (K"n)^d and [0,1]^d. Our labeling strategy lowers the upper bound on the bandwidth of the continuous Hamming graph, [0,1]^3, from .5 to .4497. A lower bound of .4439 on bw([0,1]^3) follows from known isoperimetric inequalities and a related dynamic program is conjectured to raise that lower bound to 4/9=.4444.... In particular, showing the power of our method, we prove that the bandwidth of K"6xK"6xK"6 is exactly 101.