Related papers: Matching Cells
The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. In this paper we completely characterize the pairs (graph, matching complex) for…
In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop harmonic conjugation in projective rectangles. We construct projective rectangles in some harmonic matroids (matroids where harmonic…
To a given nonsingular triangular matrix A with entries from a ring, we associate a weighted bipartite graph G(A) and give a combinatorial description of the inverse of A by employing paths in G(A). Under a certain condition, nonsingular…
An algorithm is presented that constructs an acyclic partial matching on the cells of a given simplicial complex from a vector-valued function defined on the vertices and extended to each simplex by taking the least common upper bound of…
We present a detailed study of the combinatorial interpretation of matrix integrals, including the examples of tessellations of arbitrary genera, and loop models on random surfaces. After reviewing their methods of solution, we apply these…
In this article we investigate the relations between three kinds of vector fields with close connection to each other. A compact orientable manifold enables us to integrate over it, which is very different from noncompact manifolds, and…
A matchbox manifold is a generalized lamination, and is a continuum whose arc-components define the leaves of a foliation of the space. The main result of this paper implies that a matchbox manifold which is manifold-like must be…
In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a…
A class of Cantor-type spaces and related geometric structures are discussed.
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
In a previous work, we gave a construction of (not necessarily realizable) oriented matroids from a triangulation of a product of two simplices. In this follow-up paper, we use a variant of Viro's patchworking to derive a topological…
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent…
A matching complex of a simple graph $G$ is a simplicial complex with faces given by the matchings of $G$. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa…
Biharmonic or polyharmonic curves and surfaces in 3-dimensional contact manifolds are investigated.
The perfect matching complex of a simple graph $G$ is a simplicial complex having facets (maximal faces) as the perfect matchings of $G$. This article discusses the perfect matching complex of polygonal line tilings and the $\left(2 \times…
In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of…
We give a general construction of triangulations starting from a walk in the quarter plane with small steps, which is a discrete version of the mating of trees. We use a special instance of this construction to give a bijection between maps…
Matching is a method of the design of experiments. If we had an even number of patients and wanted to form pairs of patients such that their ages, for example, in each pair be as close as possible, we would use nonbipartite matching. Not…
A vector field s on a Riemannian manifold M is said to be harmonic if there exists a member of a 2-parameter family of generalised Cheeger-Gromoll metrics on TM with respect to which s is a harmonic section. If M is a simply-connected…