Seymour's second neighborhood conjecture asserts that every nonempty finite simple directed graph with no pair of opposite
edges has a graph vertex 
satisfying
 |
where 
consists of the out-neighbors of 
and 
consists of the vertices
at directed distance exactly two from 
. The latter excludes 
and all members of 
.
The distinct Seymour conjecture concerns powers of Hamiltonian cycles in undirected graphs.
