10 problems

Let $G$ be a cycle of length $2\ell$ whose edges are colored with $h$ colors. Let $M_0$ and $M_1$ be the perfect matchings consisting of the even and odd edges, respectively, and l…

The red-blue matching problem asks, for a two-edge-colored graph and an integer $k$, whether it has a perfect matching containing exactly $k$ red edges. The classes $\mathcal{P}$ a…

A marriage problem is a matching problem in which agents have preference lists over potential partners; agents may have weights, and preference lists may contain ties. The popular…

Let $Q_1,\ldots,Q_n$ be points and let $B_1,\ldots,B_n$ be edges of a convex hull, with each point matched to one edge and the resulting triangles considered as in the preceding he…

Let two sets of points in the unit interval be ordered by their order statistics, and let the cost of a matching be given by a concave function of the distance between matched poin…

Let $P$ be a set of $2n$ uncolored points in the plane, and let $\{(a_i,b_i),i=1,\dots,n\}$ be a maximum-sum matching of $P$, meaning a matching that maximizes the total Euclidean…

A generalized $\beta$-transformation has parameters $\beta>1$ and $\alpha\in[0,1]$. It has matching if there exists a finite integer $n$ such that … The smallest such $n$ is called…

Consider the reversed two-stage procedure in which eligible units are first matched into groups of size $k'$, their centroids are then matched into homogeneous groups of size $k$,…

Let $G_n$ be a sequence of graphs admitting a graphon limit $\mathcal{G}$, with edge weights following a distribution of pseudo-dimension $q$. Suppose that there exists…

For $d>0$, let $M_n$ be the minimum total cost of a perfect matching in the pseudo-dimension $d$ mean-field model, and write $\beta_M(d)$ for the limiting average cost per vertex w…