Extremal Sets Minimizing Dimension-Normalized Boundary in Hamming Graphs

Authors:
M. Cemil Azizouglu;Ömer Eugeciouglu
Affiliations:
-;-
Venue:
SIAM Journal on Discrete Mathematics
Year:
2004

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Abstract

We prove that the set of first k vertices of a Hamming graph in reverse-lexicographic order constitutes an extremal set minimizing the dimension-normalized edge-boundary over all k-vertex subsets of the graph. This generalizes a result of Lindsey and can be used to prove a tight lower bound for the isoperimetric number and the bisection width of arrays.