Bipartite graphs can be, but I'm not proficient. I feel this is an annoying problem, but learning network flow had to learn it. Hard to chew it.
People are more stupid, so only a few days to think understood as follows. I hope to persuade or convince you.
Determining omitted bipartite graph is a graph may be divided into a bipartite graph if and only if it does not exist among the odd ring,
Maximum Matching: This is the match two points together and we demand the maximum matching a figure. Looking for augmenting paths.
Popular point is to continue to see which points can extend outward to a point where it finds a match point would not find the words to match up to look occupied its match point who point out if you can also extend it to outwardly extending it.
Above is a very simple method for finding maximum matching. But I often notice the correctness of the algorithm, that is to say that there have augmenting paths theory who account for the current position of the superior does not exist.
Because all match points only to a point of first come first served better than anyone else who is no relation of truth. .
Next is the KM algorithm weighted bipartite graph matching: Without this algorithm I might have to learn cost flow, or direct blast search. . But although limitations of this algorithm is very large and easy to forget, or to learn about it charges not much time.
Specific see algorithm step guide. Here is my understanding of KM algorithm. Painful realization.
KM algorithm correctness:
1 KM algorithm requires that the figure is the maximum weight matching that is perfect match on the match. I think this condition either gives himself the title, either the right side are positive points and each point has even want the other side as this question, then this property can be guaranteed.
2 This algorithm is around me to qualitatively describe scaling match vertices of the process of the algorithm: First, every point and their best side right match, then find some points do not match the object, then replace the staggered tree scaling then look for the value of augmenting path again. Of course, the new road is able to communicate smallest edge weight changes.
3 After my long research I finally put my counter-examples to prove out I mean if there is a direct point on the current situation makes matching than two matched sides to replace the current match and then get match point better, the idea it is easy to come to this misunderstanding through various figures I paint I found this situation is the case of perfect match does not exist or can all use the internet KM proof to prove.
As the core is equal to a complete match on a child diagram it is the greatest it can be to think: for example, when it has not yet formed a complete match since the maximum weight matching is a perfect match so the current is certainly not an optimal solution. We put out a side (or more) of the current match weight minimal side effects is the closest to answer a set of edges and then again until the perfect match to match. Why this is the biggest? It may prove to do so to ensure that the right side of the first match has not lost and has been constantly adding while, but better than the other plus side.
In conclusion get the answer must be optimal. If you really do not understand then give it a lot better to run this limitation cost flow. .