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Question: what is known about the algorithmic aspects of optimally matching a set $\mathcal{P} = \prod\limits_{i=1}^n \left(1,\,\cdots,\,k_i\right)$ of grid-points to a set of $\prod\limits_{i=1}^nk_ …

Question: are there any algorithms, resp. what can be recommended, for calculating perfect matchings with the property that the variance of their edge's weights is minimal?

A directed cycle-cover of a digraph $D$ is in the sense of this post equivalent to a perfect matching in the related undirected biadjacency graph $B$ in which the edges connect a vertex $u$ of $D$ in …

This is a followup to my question How does the complexity of calculating the Permanent imply the NP completeness of directed 3-cycle cover? Question: who contributed problem [GT13] PARTITION INTO HAM …

The subject of the paywalled article The minimum cost perfect matching problem with conflict pair constraints (MCPMPC) are perfect matchings of minimum cost that do not contain certain pairs of edges; …

This is a follow-up question to Minimum-weight disjoint union of perfect matchings: let $G$ be a complete symmetric graph with $2n$ vertices, whose edges are mapped to their weights by $\omega()$ and …

Question: what is known about minimum/maximum weight perfect matchings in magic squares with or without special properties like e.g. being pandiagonal? I am especially interested minimal/maximal cel …

Given a complete weighted graph $G(V,E),\ |V|=2n$, calculating a minimum weight matching with $n-k$ edges can be reduced to calculating a perfect matching in $H(V+U,E+F),\ |U|=2k,\ F=(u\in U,v\in V),\ …

Question: what can be said about the existence of $2k$ regular graphs, $1\lt k$ that have a $1$-factor and a $2$-factor? Provided their existence, what is/are the smallest for $k$? The graphs must b …

The subject of this question are perfect matchings of a complete undirected graph $G(V,E), n:=\mathrm{card}(V)=2k$, without self-loops or parallel edges and $n=2k$ vertices. The objective is to determ …

Is there a sound proof of or a counter example to the following conjecture: if $\boldsymbol{A}^T=\boldsymbol{A}$ is the cost-matrix of a bipartite assignment problem with unique optimal assignment, t …

as already mentioned in the comments, that is answered by Alexander Schrijver in his publication "Counting 1-factors in regular bipartite graphs": any $k$-regular bipartite graph with $2n$ vertices h …

pyMCFSimplex seems to best fit my needs. "It is a free Python port of a Python Wrapper for MCFSimplex. pyMCFimplex is a Python-Wrapper for the C++ MCFSimplex Solver Class from the Operations Research …

Is there a counter example or proof for the claim that the lightest edge-disjoint union of a pair of perfect matchings contains the edges of the lightest perfect matching in a finite complete graph wi …

I have by accident found an interesting kind of spanner of complete symmetric graphs $G(V,E)$ with weighted edges. What I actually had planned was to implement an algorithm for calculating certain non …