Assertion: graph | /r/HasProperty | well-covered
Facets:
value: well
type: DEGREE
Source sentences:
text: It also includes, for instance, the bipartite well-covered graphs studied by Ravindra (1977) and Berge (1981): in bipartite graph without isolated vertices, both sides of any bipartition form maximal independent sets (and minimal vertex covers), so if the graph is well-covered both sides must have equally many vertices.
text: A rook's graph is well covered: if one places any set of rooks on a chessboard so that no two rooks are attacking each other, it is always possible to continue placing more non-attacking rooks until there is one on every row and column of the chessboard.
text: Testing whether a graph contains two maximal independent sets of different sizes is NP-complete; that is, complementarily, testing whether a graph is well-covered is coNP-complete.
text: Although it is easy to find maximum independent sets in graphs that are known to be well-covered, it is also NP-hard for an algorithm to produce as output, on all graphs, either a maximum independent set or a guarantee that the input is not well-covered.