  Graph coloring problems are among the most fundamental problems in parallel
and distributed computing, and have been studied extensively in both settings.
In this context, designing efficient deterministic algorithms for these
problems has been found particularly challenging.
  In this work we consider this challenge, and design a novel framework for
derandomizing algorithms for coloring-type problems in the Massively Parallel
Computation (MPC) model with sublinear space. We give an application of this
framework by showing that a recent $(degree+1)$-list coloring algorithm by
Halldorsson et al. (STOC'22) in the LOCAL model of distributed computation can
be translated to the MPC model and efficiently derandomized. Our algorithm runs
in $O(\log \log \log n)$ rounds, which matches the complexity of the state of
the art algorithm for the $(\Delta + 1)$-coloring problem.
