Assertion: graph's path | /r/CapableOf | end at same vertex
Facets:
value: without traversing any edge
type: MANNER
Source sentences:
text: only once, then there exist at most two vertices of odd degree; furthermore, if the path begins and ends at the same vertex, then no vertices will have odd degree.)
text: Hamiltonian circuitA directed graph in which the path begins and ends on the same vertex (a closed loop)
text: A path that begins and ends at the same vertex without traversing any edge more than once is called a circuit, or a closed path.
text: When there exists a path that traverses each edge exactly once such that the path begins and ends at the same vertex, the path is known as an Eulerian circuit, and the graph is known as an Eulerian graph.
text: Two well-known examples are the Chinese postman problem (the shortest path that visits each edge at least once), which was solved in the 1960s, and the traveling salesman problem (the shortest path that begins and ends at the same vertex and visits each edge exactly once), which continues to attract the attention of many researchers because of its applications in routing data, products, and people.