Assertion: graph | /r/HasProperty | hamiltonian
Facets:
value: like the graph
type: OTHER
value: if
type: OTHER
value: between the two vertices
type: LOCATION
Source sentences:
text: A graph is Hamiltonian if it contains a Hamiltonian cycle, and traceable if it contains a Hamiltonian path.
text: A graph is Hamiltonian-connected if for every pair of vertices there is a Hamiltonian path between the two vertices.
text: A graph that contains a Hamiltonian cycle is called a Hamiltonian graph.
text: Like the graph 1 above, if a graph has a path that includes every vertex exactly once, while ending at the initial vertex, the graph is Hamiltonian (is a Hamiltonian graph).
text: Like the graph 2 above, if a graph has a path that includes every vertex exactly once, but ending at another vertex than the starting one, then the graph is semi-Hamiltonian (is a semi-Hamiltonian graph).
text: Dirac and Ore's theorems basically state that a graph is Hamiltonian if it has enough edges.
text: A graph is Hamiltonian if and only if its closure is Hamiltonian.