Related papers: Finding Perfect Matchings in Bipartite Hypergraphs
We show that the problem of counting perfect matchings remains #P-complete even if we restrict the input to very dense graphs, proving the conjecture in [5]. Here "dense graphs" refer to bipartite graphs of bipartite independence number…
A perfect $K_t$-matching in a graph $G$ is a spanning subgraph consisting of vertex disjoint copies of $K_t$. A classic theorem of Hajnal and Szemer\'edi states that if $G$ is a graph of order $n$ with minimum degree $\delta(G) \ge…
We introduce a `concrete complexity' model for studying algorithms for matching in bipartite graphs. The model is based on the "demand query" model used for combinatorial auctions. Most (but not all) known algorithms for bipartite matching…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
In this paper we study conditions which guarantee the existence of perfect matchings and perfect fractional matchings in uniform hypergraphs. We reduce this problem to an old conjecture by Erd\H{o}s on estimating the maximum number of edges…
In this note we study inhomogeneous random bipartite graphs in random environment. These graphs can be thought of as an extension of the classical Erd\"os-R\'enyi random graphs in a random environment. We show that the expected number of…
Property $(P)$, introduced in recent work and rooted in the classical theory of Parter vertices, concerns the existence of a nonsingular matrix $A\in S(G)$ for which every vertex of $G$ is a $P$-vertex. Previous investigations have fully…
We present an algorithm that enumerates all the perfect matchings in a given bipartite graph G = (V,E). Our algorithm requires a constant amortized time to visit one perfect matching of G, in contrast to the current fastest algorithm,…
We investigate the space complexity of certain perfect matching problems over bipartite graphs embedded on surfaces of constant genus (orientable or non-orientable). We show that the problems of deciding whether such graphs have (1) a…
Existence of a perfect matching in a random bipartite digraph with bipartition $(V_1, V_2)$, $|V_i|=n$, is studied. The graph is generated in two rounds of random selections of a potential matching partner such that the average number of…
In the perfect tiling problem, we aim to cover the vertices of a hypergraph~$G$ with pairwise vertex-disjoint copies of a hypergraph $F$. There are three essentially necessary conditions for such a perfect tiling, which correspond to…
Hypergraphs are important objects to model ternary or higher-order relations of objects, and have a number of applications in analysing many complex datasets occurring in practice. In this work we study a new heat diffusion process in…
We characterize hyperfinite bipartite graphings that admit measurable perfect matchings. In particular, we prove that every regular hyperfinite bipartite graphing admits a measurable perfect matching if it is one-ended or the degree is odd.…
Given two $k$-graphs $H$ and $F$, a perfect $F$-packing in $H$ is a collection of vertex-disjoint copies of $F$ in $H$ which together cover all the vertices in $H$. In the case when $F$ is a single edge, a perfect $F$-packing is simply a…
In this paper we further investigate the well-studied problem of finding a perfect matching in a regular bipartite graph. The first non-trivial algorithm, with running time $O(mn)$, dates back to K\"{o}nig's work in 1916 (here $m=nd$ is the…
A hypergraph is a generalization of a graph, in which a hyperedge can connect multiple vertices, modeling complex relationships involving multiple vertices simultaneously. Hypergraph pattern matching, which is to find all isomorphic…
We prove that a fractional perfect matching in a non-bipartite graph can be written, in polynomial time, as a convex combination of perfect matchings. This extends the Birkhoff-von Neumann Theorem from bipartite to non-bipartite graphs. The…
In this paper we prove a generalized version of Hall's theorem for hypergraphs. More precisely, let H be a k-uniform k- partite hypergraph with some ordering on parts as V1, V2,..., Vk. such that the subhypergraph generated on union of V1,…
There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a…
A perfect matching in a graph $G$ is a set of nonadjacent edges covering every vertex of $G$. Motivated by recent progress on the relations between the eigenvalues and the matching number of a graph, in this paper, we aim to present a…