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A perfect matching is a matching of all the vertices of a graph. In other words, a perfect matching is a set of edges such that each vertex of the graph is incident to exactly one edge in the set.
1
vote
Disjoint perfect matchings in complete bipartite graph
For fixed $n$, you can solve the problem via integer linear programming as follows. For edge $(i,j)\in E$ and matching $k\in\{1,\dots,n-1\}$, let binary decision variable $x_{i,j,k}$ indicate whether …
0
votes
What is known about iterated matching as a TSP heuristic
For optimally merging pairs of paths, you can introduce a complete graph with one node per path and edge weight for each path pair $(i,j)$ equal to the minimum of the four possible original edge weigh …
7
votes
Accepted
Connecting $2n$ points in $\mathbb R^2$ with line segments s.t. each point belongs to exactl...
You can solve this as a minimum-weight perfect matching problem in a graph with a node for each point and an edge for each pair of points. Because the distances satisfy the triangle inequality, an op …