Before revision:  1)\omega_p{3(\omega_p + 1)}}, (\Delta+m)^{2(k + 1)\omega_p{3(\omega_p + 1)}}\right)\right) amortized work , O(\log (\Delta+m)) depth  , and O\left((\Delta+m)^{2(k + 1)\omega_p{3(\omega_p + 1)}}\right) space ) expected work and O(\log^{k-2} n) depth with high probability, and O(m + \Delta) space.
After revision:  1)\omega_p{3(\omega_p + 1)}}, (\Delta+m)^{2(k + 1)\omega_p{3(\omega_p + 1)}}\right)\right) amortized work , O(\log (\Delta+m)) depth , and O\left((\Delta+m)^{2(k + 1)\omega_p{3(\omega_p + 1)}}\right) space . Using a recently developed parallel k-clique counting algorithm, we also obtain a simple batch-dynamic algorithm for k-clique counting on graphs with arboricity \alpha running in O(\Delta(m+\Delta)\alpha^{k-4) expected work and O(\log^{k-2} n) depth with high probability, and O(m + \Delta) space.