Related papers: NC Algorithms for Computing a Perfect Matching and…
A $k$-defective clique of an undirected graph $G$ is a subset of its vertices that induces a nearly complete graph with a maximum of $k$ missing edges. The maximum $k$-defective clique problem, which asks for the largest $k$-defective…
For planar graphs, it is well known that high connectivity implies a Hamiltonian cycle and hence any 4-connected planar graph has a near-perfect matching. Nevertheless, whether 6-connected 1-planar graphs admit near-perfect matchings…
For all practical purposes, the Micali-Vazirani general graph maximum matching algorithm is still the most efficient known algorithm for the problem. The purpose of this paper is to provide a complete proof of correctness of the algorithm…
The Micali-Vazirani (MV) algorithm for maximum cardinality matching in general graphs, which was published in 1980 \cite{MV}, remains to this day the most efficient known algorithm for the problem. This paper gives the first complete and…
We present an efficient algorithm for the min-max correlation clustering problem. The input is a complete graph where edges are labeled as either positive $(+)$ or negative $(-)$, and the objective is to find a clustering that minimizes the…
We propose a new greedy algorithm for the maximum cardinality matching problem. We give experimental evidence that this algorithm is likely to find a maximum matching in random graphs with constant expected degree c>0, independent of the…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
Graphs provide a natural way to represent data by encoding information about objects and the relationships between them. With the ever-increasing amount of data collected and generated, locating specific patterns of relationships between…
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…
We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let…
A perfect matching cut is a perfect matching that is also a cutset, or equivalently a perfect matching containing an even number of edges on every cycle. The corresponding algorithmic problem, Perfect Matching Cut, is known to be…
In 2005, Goddard, Hedetniemi, Hedetniemi and Laskar [Generalized subgraph-restricted matchings in graphs, Discrete Mathematics, 293 (2005) 129 - 138] asked the computational complexity of determining the maximum cardinality of a matching…
We investigate the time-complexity of the All-Pairs Max-Flow problem: Given a graph with $n$ nodes and $m$ edges, compute for all pairs of nodes the maximum-flow value between them. If Max-Flow (the version with a given source-sink pair…
We propose two fixed-parameter tractable algorithms for the weighted Max-Cut problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane…
A celebrated theorem of Pippenger, and Frankl and R\"odl states that every almost-regular, uniform hypergraph $\mathcal{H}$ with small maximum codegree has an almost-perfect matching. We extend this result by obtaining a ``conflict-free''…
We describe and analyse a simple greedy algorithm \2G\ that finds a good 2-matching $M$ in the random graph $G=G_{n,cn}^{\d\geq 3}$ when $c\geq 15$. A 2-matching is a spanning subgraph of maximum degree two and $G$ is drawn uniformly from…
We establish the expressibility in fixed-point logic with counting (FPC) of a number of natural polynomial-time problems. In particular, we show that the size of a maximum matching in a graph is definable in FPC. This settles an open…
We study the problem of finding a maximum matching in a graph given by an input stream listing its edges in some arbitrary order, where the quantity to be maximized is given by a monotone submodular function on subsets of edges. This…
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure…
A $k$-clique is a dense graph, consisting of $k$ fully-connected nodes, that finds numerous applications, such as community detection and network analysis. In this paper, we study a new problem, that finds a maximum set of disjoint…