  We present the analysis of the color-magnitude relation (CMR) for a sample of
57 X-ray detected Abell clusters within the redshift interval 0.02 <= z <=
0.18. We use the B-R vs R color-magnitude plane to establish that the CMR is
present in all our low-redshift clusters and can be parameterized by a single
straight line.We find that the CMRs for this large cluster sample of different
richness and cluster types are consistent with having universal properties. The
k-corrected color of the individual CMRs in the sample at a fixed absolute
magnitude have a small intrinsic dispersion of ~0.05 mag. The slope of the CMR
is consistent with being the same for all clusters, with the variations
entirely accountable by filter band shifting effects. We determine the mean of
the dispersion of the 57 CMRs to be 0.074 mag, with a small rms scatter of
0.026 mag. However, a modest amount of the dispersion arises from photometric
measurement errors and possible background cluster superpositions; and the
derived mean dispersion is an upper limit. Models which explain the CMR in
terms of metallicity and passive evolution can naturally reproduce the observed
behavior of the CMR in this paper. The observed properties of the CMR are
consistent with models in which the last episode of significant star formation
in cluster early-type galaxies occurred significantly more than ~3 Gyr ago, and
that the core set of early-type galaxies in clusters were formed more than 7
Gyr ago. (abridged)
