Related papers: On Counting Perfect Matchings in General Graphs
The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree…
Given a bipartite graph, the maximum balanced biclique (\textsf{MBB}) problem, discovering a mutually connected while equal-sized disjoint sets with the maximum cardinality, plays a significant role for mining the bipartite graph and has…
This work is the PhD thesis of Nicolas Trotignon, written in 2004 under the supervision of Fr\'ed\'eric Maffray. It is motivated by the desire for a better understanding of perfect graphs. The proof of the Claude Berge's perfect graph…
Subgraph matching is a compute-intensive problem that asks to enumerate all the isomorphic embeddings of a query graph within a data graph. This problem is generally solved with backtracking, which recursively evolves every possible partial…
We present a novel local improvement scheme for the perfectly balanced graph partitioning problem. This scheme encodes local searches that are not restricted to a balance constraint into a model allowing us to find combinations of these…
Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first…
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 consider a matching problem in a bipartite graph $G$ where every vertex has a capacity and a strict preference order on its neighbors. Furthermore, there is a cost function on the edge set. We assume $G$ admits a perfect matching, i.e.,…
In network modeling of complex systems one is often required to sample random realizations of networks that obey a given set of constraints, usually in form of graph measures. A much studied class of problems targets uniform sampling of…
We identify and study relevant structural parameters for the problem PerfMatch of counting perfect matchings in a given input graph $G$. These generalize the well-known tractable planar case, and they include the genus of $G$, its apex…
We exactly settle the complexity of graph realization, graph rigidity, and graph global rigidity as applied to three types of graphs: "globally noncrossing" graphs, which avoid crossings in all of their configurations; matchstick graphs,…
Let $G=(V,E)$ be a graph and let $A_G$ be the clique-vertex incidence matrix of $G$. It is well known that $G$ is perfect iff the system $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$ is totally dual integral (TDI). In 1982, Cameron…
Counting the number of perfect matchings in bipartite graphs, or equivalently computing the permanent of 0-1 matrices, is an important combinatorial problem that has been extensively studied by theoreticians and practitioners alike. The…
We reprove that all the matchings constructed during Edmonds' weighted perfect matching algorithm are optimal among those of the same cardinality (provided that certain mild restrictions are obeyed on the choices the algorithm makes). We…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…
We propose an improved algorithm for counting the number of Hamiltonian cycles in a directed graph. The basic idea of the method is sequential acceptance/rejection, which is successfully used in approximating the number of perfect matchings…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…
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…
Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for…
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…