  The Caccetta-Haggkvist conjecture made in 1978 asserts that every orgraph on
n vertices without oriented cycles of length <= l must contain a vertex of
outdegree at most (n-1)/l. It has a rather elaborate set of (conjectured)
extremal configurations.
  In this paper we consider the case l=3 that received quite a significant
attention in the literature. We identify three orgraphs on four vertices each
that are missing as an induced subgraph in all known extremal examples and
prove the Caccetta-Haggkvist conjecture for orgraphs missing as induced
subgraphs any of these orgraphs, along with cycles of length 3. Using a
standard trick, we can also lift the restriction of being induced, although
this makes graphs in our list slightly more complicated.
