Does Dirac's theorem on Hamiltonian cycles only apply to undirected graphs? Does Dirac's theorem on Hamiltonian cycles only apply for undirected graphs? If the theorem applied to directed graphs, the graph with the following adjacency list should have a Hamiltonian cycle, but I can't find one.


  $0$: $1$ $2$ $3$
  
  $1$: $2$ $3$
  
  $2$: $1$ $3$
  
  $3$: $1$ $2$
While Dirac's theorem wasn't intended/proved for directed graphs, it was extended to directed graphs by GHOUILA-HOURI in 1960 ("Une condition suffisante d’existence d'un circuit hamiltonien").

Their requirements, however, were that each vertex should have both out-degree and in-degree of at least $n/2$, which is not the case in your graph.

One of the original conditions of GHOUILA-HOURI, as Saeed mentioned, is that the graph is strongly connected. In fact, the degree conditions are strong enough for only diameter $\leq 2$ graphs to be considered.