Assertion: graph's set | /r/HasAspect | nonempty intersection
Facets:
value: if
type: DEGREE
Source sentences:
text: by creating one vertex v i for each set S i , and connecting two vertices v i and v j by an edge whenever the corresponding two sets have a nonempty intersection, that is,
text: Any undirected graph G may be represented as an intersection graph: for each vertex v i of G, form a set S i consisting of the edges incident to v i ; then two such sets have a nonempty intersection if and only if the corresponding vertices share an edge.
text: In the same way that an intersection representation of a graph labels every vertex with a set so that vertices are adjacent if and only if their sets have nonempty intersection, so an inclusion representation f of a poset labels every element with a set so that for any x and y in the poset, x