相关论文: Jamming and geometric representations of graphs

An exact description of the complete jamming landscape is developed for a system of hard discs of diameter $\sigma$, confined between two lines separated by a distance $1+\sqrt{3/4} < H/\sigma < 2$. By considering all possible local packing…

Colloidal and other granular media experience a transition to rigidity known as jamming if the fill fraction is increased beyond a critical value. The resulting jammed structures are locally disordered, bear applied loads inhomogenously,…

Tutte's celebrated barycentric embedding theorem describes a natural way to build straight-line embeddings (crossing-free drawings) of a (3-connected) planar graph: map the vertices of the outer face to the vertices of a convex polygon, and…

We investigate the existence of random close and random loose packing limits in two-dimensional packings of monodisperse hard disks. A statistical mechanics approach-- based on several approximations to predict the probability distribution…

In this survey of graph polynomials, we emphasize the Tutte polynomial and a selection of closely related graph polynomials. We explore some of the Tutte polynomial's many properties and applications and we use the Tutte polynomial to…

We study the problem of finding the minimal (maximal) genus for a surface where a given four-valent graph with fixed opposite edge structure can be embedded into. We find several partial relations and give new reformulations in…

A granular-matter model is exactly solved, where disks of two sizes and weights in alternating sequence are confined to a narrow channel. The axis of the channel is horizontal and its plane vertical. Disk sizes and channel width are such…

Grafting is a surgery on Riemann surfaces introduced by Thurston which connects hyperbolic geometry and the theory of projective structures on surfaces. We will discuss the space of projective structures in terms of the Thurston's geometric…

There are several different extensions of the Tutte polynomial to graphs embedded in surfaces. To help frame the different options, here we consider the problem of extending the Tutte polynomial to cellularly embedded graphs starting from…

This paper surveys a comprehensive, although not exhaustive, sampling of graph polynomials with the goal of providing a brief overview of a variety of techniques defining a graph polynomial and then for decoding the combinatorial…

We take an elementary and systematic approach to the problem of extending the Tutte polynomial to the setting of embedded graphs. Four notions of embedded graphs arise naturally when considering deletion and contraction operations on graphs…

We introduce a new optimization problem regarding embeddings of a graph into a Euclidean space and discuss its relation to the two, mutually dual, optimizations problems introduced by Goering-Helmberg-Wappler. We prove that the Laplace…

We describe an infinite family of edge-decompositions of complete graphs into two graphs, each of which triangulate the same orientable surface. Previously, such decompositions had only been known for only a few complete graphs. These…

Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…

Graph embeddings deal with injective maps from a given simple, undirected graph $G=(V,E)$ into a metric space, such as $\mathbb{R}^n$ with the Euclidean metric. This concept is widely studied in computer science, see \cite{ge1}, but also…

Given a graph and a representation of its fundamental group, there is a naturally associated twisted adjacency operator. The main result of this article is the fact that these operators behave in a controlled way under graph covering maps.…

Simultaneous embedding is concerned with simultaneously representing a series of graphs sharing some or all vertices. This forms the basis for the visualization of dynamic graphs and thus is an important field of research. Recently there…

This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…

Jamming refers to the deletion, corruption or damage of meter measurements that prevents their further usage. This is distinct from adversarial data injection that changes meter readings while preserving their utility in state estimation.…

We present a jamming diagram for 2D bidisperse granular systems, capturing two distinct jamming transitions. The first occurs as large particles form a jammed structure, while the second, emerging at a critical small-particle concentration,…