Minimum path cover
The number of sides of the split point and out-points, the minimum path coverage = original artwork - a new maximum matching of FIG.
Minimum Vertex Cover bipartite FIG.
Minimum Vertex Cover = Maximum Matching
Bipartite graph maximum independent set
= Maximum independent set points - Minimum Vertex Cover
FIG bipartite minimum edge covering
Points = smallest side cover - Minimum Vertex Cover
FIG minimum point right bipartite cover
Original bipartite graph edge (u, v) is replaced with a capacity of INF directed edge (u, v), the establishment of the source point s and the sink t, connecting the s and x in the set point, the capacity for points weight; the same point in the y t are connected, the weight capacity of that point. Seeking new maximum flow in FIG., The maximum flow rate is the minimum point of the right weight and the coverage value.
Maximum weight bipartite graph independent set
Independent set maximum weight = total weight - Minimum Vertex Cover