  We settle the complexity of the $(\Delta+1)$-coloring and $(\Delta+1)$-list
coloring problems in the CONGESTED CLIQUE model by presenting a simple
deterministic algorithm for both problems running in a constant number of
rounds. This matches the complexity of the recent breakthrough randomized
constant-round $(\Delta+1)$-list coloring algorithm due to Chang et al.
(PODC'19), and significantly improves upon the state-of-the-art $O(\log
\Delta)$-round deterministic $(\Delta+1)$-coloring bound of Parter (ICALP'18).
  A remarkable property of our algorithm is its simplicity. Whereas the
state-of-the-art randomized algorithms for this problem are based on the quite
involved local coloring algorithm of Chang et al. (STOC'18), our algorithm can
be described in just a few lines. At a high level, it applies a careful
derandomization of a recursive procedure which partitions the nodes and their
respective palettes into separate bins. We show that after $O(1)$ recursion
steps, the remaining uncolored subgraph within each bin has linear size, and
thus can be solved locally by collecting it to a single node. This algorithm
can also be implemented in the Massively Parallel Computation (MPC) model
provided that each machine has linear (in $n$, the number of nodes in the input
graph) space.
  We also show an extension of our algorithm to the MPC regime in which
machines have sublinear space: we present the first deterministic
$(\Delta+1)$-list coloring algorithm designed for sublinear-space MPC, which
runs in $O(\log \Delta + \log\log n)$ rounds.
