clique cover造句

• The equality of the intersection number and the edge clique cover number is straightforward to prove.
• The clique cover problem concerns finding as few cliques as possible that include every vertex in the graph.
• Another class of graphs in which the minimum clique cover can be found in polynomial time are the triangle-free graphs.
• Therefore, in triangle-free graphs, the minimum clique cover can be found by using an algorithm for maximum matching.
• Thus, a clique in the original graph becomes an independent set in the complement and a coloring of the original graph becomes a clique cover of the complement.
• In these graphs, every clique cover consists of a matching ( a set of disjoint pairs of adjacent vertices ) together with singleton sets for the remaining unmatched vertices.
• Thus, perfection ( defined as the equality of maximum clique size and chromatic number in every induced subgraph ) is equivalent to the equality of maximum independent set size and clique cover number.
• The equivalence between clique covers and coloring is a reduction that can be used to prove the NP-completeness of the clique cover problem from the known NP-completeness of graph coloring.
• The equivalence between clique covers and coloring is a reduction that can be used to prove the NP-completeness of the clique cover problem from the known NP-completeness of graph coloring.
• For instance, a well-covered 3-connected maximal planar graph may be obtained via the clique cover construction from any-vertex maximal planar graph in which there are disjoint triangle faces by adding new vertices, one within each of these faces.
• More generally, given any graph together with a clique cover ( a partition of the vertices of into cliques ), the graph formed by adding another vertex to each clique is well-covered; the rooted product is the special case of this construction when consists of one-vertex cliques.
• Therefore, the graph formed from " G " by removing " K " has clique cover number at most one less than the clique number of " G ", and independence number at least one less than the independence number of " G ", and the result follows by induction on this number.