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Bookmark or Share- Perfect matching in a tree - Mathematics Stack ExchangeProve 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...
- 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?
- Perfect matching problem - Computer Science Stack ExchangeI 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.
- Proving every tree has at most one perfect matchingTree with even no of vertices will have the perfect matching as all the vertices with same color can be grouped together and a matching can be established between two groups. But any tree with odd no of vertex will have no perfect matching for obvious reason.
- Perfect matching in the Petersen graph - Mathematics Stack ExchangeHere, 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 ...
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