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$: $1$ $2$
Does Dirac's theorem on Hamiltonian cycles only apply to undirected graphs?
graph theory
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 dexistence 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.