Clusters of galaxies are believed to be at the intersections of cosmological filaments and to grow by accreting matter from these filaments. Such continuous infall has major consequences not only on clusters but also on the physics of cluster galaxies. Faint galaxies are particularly interesting as they are very sensitive to environmental effects, and may have a different behaviour from that of bright galaxies. The aim of this paper is to sample the Coma cluster building history, based on the analysis of galaxy luminosity functions and red sequences in the Color Magnitude Relation down to faint magnitudes, which are privileged tools for this purpose. The present analysis is based on deep (R~24), wide (~0.5 deg2) multiband (BVRI Vega system) images of the Coma cluster obtained with the CFH12K camera at the CFHT. We have derived LFs and CMRs in twenty 10x10 arcmin2 regions and in larger regions. In all photometric bands, we found steeply rising LFs in the north-northeast half of the cluster (due to early type galaxies at bright magnitudes and due to late type galaxies at the faint end), and much flatter LFs in the south-southwest region. Although the fine behaviour of the CMR RS is different in these two regions, a good agreement is found in general between the RS computed for faint and for bright galaxies. All these results can be interpreted consistently in the framework of the building up process previously proposed. The Northern Coma area is a relatively quiescent region while the southern area experiences several infalls.
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