Concept of Bipartite Graph

Bipartite Graph: the vertex of a graph can be divided into two sets, X and Y. Among the two vertices associated with all edges, exactly one belongs to X and the other belongs to y. Nodes in the same set are not adjacent.

Matching: a matching graph is a set of some edges, and any two edges have no common points.

Maximum match: match with the largest number of contained edges. HungaryAlgorithm

Perfect match: all vertices are matched on the edge.

Complete match: In the bipartite graph, all vertices in x match accordingly or all vertices in the Y set match accordingly.

Optimal Match: If G is a weighted bipartite graph, the perfect match between the weight value and the maximum value is called the best match. KM Algorithm

Minimum coverage: use the least number of vertices (x set or y set) to associate each edge with at least one of the vertices. That is, the overwriting edge. Least point (overwrite) = maximum number of matches

Minimum path overwrite: overwrite all nodes in directed acyclic graph G with a few non-Intersecting simple paths. That is, the coverage point. Create a bipartite graph model and split all vertex I into two:
''. If edge I-> J exists, edge I-> J is introduced in the bipartite graph, and the result is the minimum path overwrite = N-Maximum number of matches. (N indicates the number of knots in the source image)

Maximum Independent Set: m points are selected in the graph of N points so that there is no edge between the M points. calculates the maximum m value. if it is a bipartite graph, then. maximum Independent Set = N-Maximum number of matches.

Full subgraph: a set of vertices connected to any two points

Maximum number of vertices: the maximum number of vertices in the largest complete subgraph = the maximum number of independent parts of the source image. (isn't the independent set in the complement graph having no edge to each other? On the other hand, are they connected to edges in the source image)

Bipartite Graph: the vertex of a graph can be divided into two sets, X and Y. Among the two vertices associated with all edges, exactly one belongs to X and the other belongs to y. Nodes in the same set are not adjacent.

Matching: a matching graph is a set of some edges, and any two edges have no common points.

Maximum match: match with the largest number of contained edges. Hungary Algorithm

Perfect match: all vertices are matched on the edge.

Complete match: In the bipartite graph, all vertices in x match accordingly or all vertices in the Y set match accordingly.

Optimal Match: If G is a weighted bipartite graph, the perfect match between the weight value and the maximum value is called the best match. KM Algorithm

Minimum coverage: use the least number of vertices (x set or y set) to associate each edge with at least one of the vertices. That is, the overwriting edge. Least point (overwrite) = maximum number of matches

Minimum path overwrite: overwrite all nodes in directed acyclic graph G with a few non-Intersecting simple paths. That is, the coverage point. Create a bipartite graph model and split all vertex I into two:
''. If edge I-> J exists, edge I-> J is introduced in the bipartite graph, and the result is the minimum path overwrite = N-Maximum number of matches. (N indicates the number of knots in the source image)

Maximum Independent Set: m points are selected in the graph of N points so that there is no edge between the M points. calculates the maximum m value. if it is a bipartite graph, then. maximum Independent Set = N-Maximum number of matches.

Full subgraph: a set of vertices connected to any two points

Maximum number of vertices: the maximum number of vertices in the largest complete subgraph = the maximum number of independent parts of the source image. (isn't the independent set in the complement graph having no edge to each other? On the other hand, are they connected to edges in the source image)