  Triangle-free graphs play a central role in graph theory, and triangle
detection (or triangle finding) as well as triangle enumeration (triangle
listing) play central roles in the field of graph algorithms. In distributed
computing, algorithms with sublinear round complexity for triangle finding and
listing have recently been developed in the powerful CONGEST clique model,
where communication is allowed between any two nodes of the network. In this
paper we present the first algorithms with sublinear complexity for triangle
finding and triangle listing in the standard CONGEST model, where the
communication topology is the same as the topology of the network. More
precisely, we give randomized algorithms for triangle finding and listing with
round complexity $O(n^{2/3}(\log n)^{2/3})$ and $O(n^{3/4}\log n)$,
respectively, where $n$ denotes the number of nodes of the network. We also
show a lower bound $\Omega(n^{1/3}/\log n)$ on the round complexity of triangle
listing, which also holds for the CONGEST clique model.
