Assertion: graph | /r/HasAspect | vertex
Facets:
value: with high degree
type: OTHER
value: for each member of s
type: OTHER
value: for each line segment in s
type: LOCATION
value: as a base case
type: MANNER
value: for each curve
type: OTHER
Source sentences:
text: Given a graph G, G is a string graph if and only if there exists a set of curves, or strings, drawn in the plane such that no three strings intersect at a single point and such that the graph having a vertex for each curve and an edge for each intersecting pair of curves is isomorphic to G.
text: In arbitrary graphs, listing all triangles sometimes requires Ω(m3/2) time, as some graphs have that many triangles, however Hagauer et al.
text: As a base case, the graph has only one vertex.
text: The same method of translating partial orders into DAGs works more generally: for every finite partially ordered set (S, ≤), the graph that has a vertex for each member of S and an edge for each pair of elements related by u ≤ v is automatically a transitively closed DAG, and has (S, ≤) as its reachability relation.
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: If a graph has vertices with high degree then it necessarily will have small angular resolution, but the angular resolution can be bounded below by a function of the degree.