相关论文: Symmetric contact systems of segments, pseudotrian…

Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…

Flip graphs of combinatorial and geometric objects are at the heart of many deep structural insights and connections between different branches of discrete mathematics and computer science. They also provide a natural framework for the…

Contact path geometries are curved geometric structures on a contact manifold comprising smooth families of paths modeled on the family of all isotropic lines in the projectivization of a symplectic vector space. Locally such a structure is…

This article presents a survey of some recent results in the theory of spatial graphs. In particular, we highlight results related to intrinsic knotting and linking and results about symmetries of spatial graphs. In both cases we consider…

There have been recent advances in the analysis and visualization of 3D symmetric tensor fields, with a focus on the robust extraction of tensor field topology. However, topological features such as degenerate curves and neutral surfaces do…

Simplicial surfaces describe the incidence relations between vertices, edges and faces of triangulated 2-dimensional manifolds in a purely combinatorial way. By considering only the incidences of edges and faces, simplicial surfaces are…

Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applications to the topology of braid groups, knot theory,…

We prove that a planar graph is generically rigid in the plane if and only if it can be embedded as a pseudo-triangulation. This generalizes the main result of math.CO/0307347 which treats the minimally generically rigid case. The proof…

A natural problem in combinatorial rigidity theory concerns the determination of the rigidity or flexibility of bar-joint frameworks in $\mathbb{R}^d$ that admit some non-trivial symmetry. When $d=2$ there is a large literature on this…

The Circle Pattern Theorem characterizes the existence and rigidity of circle patterns with prescribed intersection angles on simplicial triangulations of closed surfaces. In this paper we extend the theorem to quasi-simplicial…

We introduce and analyze the characteristic foliation induced by a contact structure on a branched surface, in particular a branched standard spine of a 3-manifold. We extend to (fairly general) singular foliations of branched surfaces the…

We consider {\em L-graphs}, that is contact graphs of axis-aligned L-shapes in the plane, all with the same rotation. We provide several characterizations of L-graphs, drawing connections to Schnyder realizers and canonical orders of…

A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…

We investigate properties of sparse and tight surface graphs. In particular we derive topological inductive constructions for $(2, 2)$-tight surface graphs in the case of the sphere, the plane, the twice punctured sphere and the torus. In…

In this paper, we consider the problem of representing graphs by triangles whose sides touch. As a simple necessary condition, we show that pairs of vertices must have a small common neighborhood. On the positive side, we present linear…

The intersection matrix of a finite simplicial complex has as each of its entries the rank of the intersection of its respective simplices. We prove that such matrix defines the triangulation of a closed connected surface up to isomorphism.

Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…

We consider the problem of morphing between contact representations of a plane graph. In an $\mathcal F$-contact representation of a plane graph $G$, vertices are realized by internally disjoint elements from a family $\mathcal F$ of…

The conductance through a quantum point contact created by a sharp and hard metal tip on the graphite surface has features which to our knowledge have not been encountered so far in metal contacts or in nanowires. In this paper we first…

Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs.…