On the bandwidth of 3-dimensional Hamming graphs

This paper presents strategies for improving the known upper and lower bounds for the bandwidth of Hamming graphs (Kn)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

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: J. Balogh, Sergei L. Bezrukov, L. H. Harper, Ákos Seress
• Keywords: Continuous Hamming Graph, Lower Bound, TCS 2008, Theoretical Computer Science, Upper Bound