  We examine the alignment between Brightest Cluster Galaxies (BCGs) and their
host clusters in a sample of 7031 clusters with 0.08<z<0.44 found using a
matched-filter algorithm and an independent sample of 5744 clusters with
0.1<z<0.3 selected with the maxBCG algorithm, both extracted from the Sloan
Digital Sky Survey Data Release 6 imaging data. We confirm that BCGs are
preferentially aligned with the cluster's major axis; clusters with dominant
BCGs (>0.65 mag brighter than the mean of the second and third ranked galaxies)
show stronger alignment than do clusters with less dominant BCGs at the 4.4
sigma level. Rich clusters show a stronger alignment than do poor clusters at
the 2.3 sigma level. Low redshift clusters (z<0.26) show more alignment than do
high redshift (z>0.26) clusters, with a difference significant at the 3.0 sigma
level. Our results do not depend on the algorithm used to select the cluster
sample, suggesting that they are not biased by systematics of either algorithm.
The correlation between BCG dominance and cluster alignment may be a
consequence of the hierarchical merging process which forms the cluster. The
observed redshift evolution may follow from secondary infall at late redshifts.
