Assertion: graph | /r/HasProperty | tree-like
Facets:
value: locally
type: LOCATION
Source sentences:
text: The same characterization applies to graphs that are locally tree-like, in the sense that low-diameter neighborhoods of every vertex are acyclic: if a graph has girth eight or more (so that, for every vertex v, the subgraph of vertices within distance three of v is acyclic) then it is well-covered if and only if every vertex of degree greater than one has exactly one neighbor of degree one.