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graph theory - Perfect matching and maximum matching - Mathematics . . . Indeed a perfect matching is an example of a maximum matching; this follows from the definitions: A perfect matching is a matching which matches all vertices of the graph A maximum matching is a matching that contains the largest possible number of edges If we added an edge to a perfect matching it would no longer be a matching
Perfect matching in a graph and complete matching in bipartite graph . . . These are two different concepts A perfect matching is a matching involving all the vertices A bipartite perfect matching (especially in the context of Hall's theorem) is a matching in a bipartite graph which involves completely one of the bipartitions If the bipartite graph is balanced – both bipartitions have the same number of vertices
How to find the number of perfect matchings in complete graphs? $\begingroup$ @Srivatsan in one of the books I have, the solution is same, but it explains it as: "The number of perfect matchings in a complete graph of n vertices, where n is even, reduces to the problem of finding unordered partitions of vertex set of the type p(2n;2,2,2, n times) = $\frac{(2n)!}{(2!)^nn!}$ ", Is p(2n;2,2,2, n times) some series?
Prove that a $k$-regular bipartite graph has a perfect matching Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
How to determine if a tree $T = (V, E)$ has a perfect matching in $O(|V . . . If there is one (B) and everything else is (A), then you can match that vertex with the root and the result is (A) Finally, if the tree is connected to more than one (B), it can't be covered (C) This is a recursive traversal of the tree, which can be done in linear time
Perfect matching in the Petersen graph - Mathematics Stack Exchange Here, the six perfect matchings come in two families of three (where each family consists of three rotations of the same matching) Because it's impossible to have a rotationally symmetric perfect matching in this drawing (the central vertex can only be matched to one of the outside vertices) it's easy to see that the number of perfect
Perfect matching problem - Computer Science Stack Exchange I want to find some perfect matching with some given cost I suspect that this is hard (i e NP-complete) Can you solve it quickly? (find an efficient algorithm) Here is an example: we have three courses, credit hours are 4, 5, 8 Grade points are 4, 3, 2 A solution is a perfect matching between the lists that result in some given GPA
Perfect matching in a tree - Mathematics Stack Exchange Prove that in a tree there is at most $1$ perfect matching If the number of vertices is even$\implies$ number of edges odd, not divisible by $2$, so no perfect matching For the other case can you apply induction using $2$ leaves ?
Perfect matching of a tree - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers