Assertion: graph's g | /r/HasProperty | covered
Facets:
value: very well
type: DEGREE
value: has with the property
type: OTHER
value: in polynomial time
type: OTHER
value: if
type: DEGREE
Source sentences:
text: G is very well covered if and only if it has a perfect matching M with the following two properties:
text: If P is either a polygon or a set of points, S is the set of open line segments that have vertices of P as endpoints and are otherwise disjoint from P, and G is the intersection graph of S (a graph that has a vertex for each line segment in S and an edge for each two line segments that cross each other), then G is well-covered.
text: Moreover, if G is very well covered, then every perfect matching in G satisfies these properties.
text: G is very well covered in polynomial time.
text: G is well-covered if and only if it has a perfect matching M with the property that, for every edge uv in M, the induced subgraph of the neighbors of u and v forms a complete bipartite graph.