  The importance of classifying connections in large graphs has been the
motivation for a rich line of work on distributed subgraph finding that has led
to exciting recent breakthroughs. A crucial aspect that remained open was
whether deterministic algorithms can be as efficient as their randomized
counterparts, where the latter are known to be tight up to polylogarithmic
factors.
  We give deterministic distributed algorithms for listing cliques of size $p$
in $n^{1 - 2/p + o(1)}$ rounds in the \congest model. For triangles, our
$n^{1/3+o(1)}$ round complexity improves upon the previous state of the art of
$n^{2/3+o(1)}$ rounds [Chang and Saranurak, FOCS 2020]. For cliques of size $p
\geq 4$, ours are the first non-trivial deterministic distributed algorithms.
Given known lower bounds, for all values $p \geq 3$ our algorithms are tight up
to a $n^{o(1)}$ subpolynomial factor, which comes from the deterministic
routing procedure we use.
