Related papers: Maximum matching on random graphs
The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…
We present an algorithm that finds a maximum cardinality $f$-matching of a simple graph in time $O(n^{2/3} m)$. Here $f:V\to \mathbb{N}$ is a given function, and an $f$-matching is a subgraph wherein each vertex $v\in V$ has degree $\le…
Graph matching is the process of computing the similarity between two graphs. Depending on the requirement, it can be exact or inexact. Exact graph matching requires a strict correspondence between nodes of two graphs, whereas inexact…
A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs contain a perfect matching.
A matching in a graph is uniquely restricted if no other matching covers exactly the same set of vertices. We establish tight lower bounds on the maximum size of a uniquely restricted matching in terms of order, size, and maximum degree.
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
It was conjectured by Mkrtchyan, Petrosyan, and Vardanyan that every graph $G$ with $\Delta(G)-\delta(G) \le 1$ has a maximum matching $M$ such that any two $M$-unsaturated vertices do not share a neighbor. In this note, we confirm the…
This paper formulates a necessary and sufficient condition for a generic graph matching problem to be equivalent to the maximum vertex and edge weight clique problem in a derived association graph. The consequences of this results are…
Consider a random graph model where each possible edge $e$ is present independently with some probability $p_e$. Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we…
We give an upper bound on the number of perfect matchings in an undirected simple graph $G$ with an even number of vertices, in terms of the degrees of all the vertices in $G$. This bound is sharp if $G$ is a union of complete bipartite…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
A matching is a set of edges without common endpoint. It was recently shown that every 1-planar graph (i.e., a graph that can be drawn in the plane with at most one crossing per edge) that has minimum degree 3 has a matching of size at…
In this paper we rigorously prove the validity of the cavity method for the problem of counting the number of matchings in graphs with large girth. Cavity method is an important heuristic developed by statistical physicists that has lead to…
We introduce and study a new optimization problem called Hyper Vertex Cover. This problem is a generalization of the standard vertex cover to hypergraphs: one seeks a configuration of particles with minimal density such that every hyperedge…
Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the computer…
The edge domination number $\gamma_e(G)$ of a graph $G$ is the minimum size of a maximal matching in $G$. It is well known that this parameter is computationally very hard, and several approximation algorithms and heuristics have been…
The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and…
Suppose that we are given an arbitrary graph $G=(V, E)$ and know that each edge in $E$ is going to be realized independently with some probability $p$. The goal in the stochastic matching problem is to pick a sparse subgraph $Q$ of $G$ such…
This paper presents an $O(\log\log \bar{d})$ round massively parallel algorithm for $1+\epsilon$ approximation of maximum weighted $b$-matchings, using near-linear memory per machine. Here $\bar{d}$ denotes the average degree in the graph…
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…