  For two massless particles i and j, the collinear limit is a special
kinematic configuration in which the particles propagate with parallel
four-momentum vectors, with the total momentum P distributed as p_i=xP and
p_j=(1-x)P, so that s_{ij}=(p_i+p_j)^2=P^2=0. In Yang-Mills theory, if i and j
are among N gauge bosons participating in a scattering process, it is well
known that the partial amplitudes associated to the (single trace) group
factors with adjacent i and j are singular in the collinear limit and factorize
at the leading order into N-1-particle amplitudes times the universal,
x-dependent Altarelli-Parisi factors. We give a precise definition of the
collinear limit and show that at the tree level, the subleading, non-singular
terms are related to the amplitudes with a single graviton inserted instead of
two collinear gauge bosons. To that end, we argue that in one-graviton
Einstein-Yang-Mills amplitudes, the graviton with momentum P can be replaced by
a pair of collinear gauge bosons carrying arbitrary momentum fractions xP and
(1-x)P.
