  Combining data from the ACS Virgo Cluster Survey (ACSVCS) and the Next
Generation Virgo cluster Survey (NGVS), we extend previous studies of color
gradients of the globular cluster (GC) systems of the two most massive galaxies
in the Virgo cluster, M87 and M49, to radii of $\sim 15~R_e$ ($\sim 200$ kpc
for M87 and $\sim 250$ kpc for M49). We find significant negative color
gradients, i.e., becoming bluer with increasing distance, out to these large
radii. The gradients are driven mainly by the outwards decrease of the ratio of
red to blue GC numbers. The color gradients are also detected out to $\sim
15~R_e$ in the red and blue sub-populations of GCs taken separately. In
addition, we find a negative color gradient when we consider the satellite
low-mass elliptical galaxies as a system, i.e., the satellite galaxies closer
to the center of the host galaxy usually have redder color indices, both for
their stars and GCs. According to the "two phase" formation scenario of massive
early-type galaxies, the host galaxy accretes stars and GCs from low-mass
satellite galaxies in the second phase. So the accreted GC system naturally
inherits the negative color gradient present in the satellite population. This
can explain why the color gradient of the GC system can still be observed at
large radii after multiple minor mergers.
