  The gluon tree amplitudes of open twistor string theory, defined as contour
integrals over the ACCK link variables, are shown to satisfy the BCFW
relations, thus confirming that they coincide with the corresponding amplitudes
in gauge field theory. In this approach, the integration contours are specified
as encircling the zeros of certain constraint functions that force the
appropriate relation between the link variables and the twistor string
world-sheet variables. To do this, methods for calculating the tree amplitudes
using link variables are developed further including diagrammatic methods for
organizing and performing the calculations.
