相关论文: Jamming and geometric representations of graphs
We introduce the notions of arithmetic colorings and arithmetic flows over a graph with labelled edges, which generalize the notions of colorings and flows over a graph. We show that the corresponding arithmetic chromatic polynomial and…
We revisit the concept of minimal rigidity as applied to soft repulsive, frictionless sphere packings in two-dimensions with the introduction of the jamming graph. Minimal rigidity is a purely combinatorial property encoded via Laman's…
This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…
This note reviews some of the recent work on biharmonic conformal maps (see \cite{OC}, Chapter 11, for a detailed survey). It will be focused on biharmonic conformal immersions and biharmonic conformal maps between manifolds of the same…
This paper is devoted to the study of the global properties of harmonically immersed Riemann surfaces in $\mathbb{R}^3.$ We focus on the geometry of complete harmonic immersions with quasiconformal Gauss map, and in particular, of those…
We study thermodynamics properties of a one dimensional gas of hard elongated particles. The particle centers are restricted to a line, while they can rotate in two-dimensional space. Correlations between orientations of the objects are…
The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation…
We solve a problem posed by Cardinali and Sastry [2] about factorization of $2$-covers of finite classical generalized quadrangles. To that end, we develop a general theory of cover factorization for generalized quadrangles, and in…
Jamming is a fundamental transition that governs the mechanical behavior of particulate media, including sand, foam and dense suspensions but also biological tissues: Upon compression, particulate media can change from freely flowing to a…
We discuss various aspects of a local-to-global embedding technique and the metric geometry of stable metric spaces and of two of its important subclasses: locally finite spaces and proper spaces. We explain how the barycentric gluing…
Determining the number of embeddings of Laman graph frameworks is an open problem which corresponds to understanding the solutions of the resulting systems of equations. In this paper we investigate the bounds which can be obtained from the…
The maximum graph bisection problem is a well known graph partition problem. The problem has been proven to be NP-hard. In the maximum graph bisection problem it is required that the set of vertices is divided into two partition with equal…
We study methods to manipulate weights in stress-graph embeddings to improve convex straight-line planar drawings of 3-connected planar graphs. Stress-graph embeddings are weighted versions of Tutte embeddings, where solving a linear system…
We provide a matrix-based formula for the Tutte symmetric function of a graph. In particular, for any graph $G$ with a designated head and tail vertex, we describe an infinite matrix $M_G$ from which the Tutte symmetric function can be…
The ideal (tagged resp.) triangulation of bounded surface with marked points are associated with skew-symmetric (skew-symmetrizable) exchange matrices. An algo- rithm is established to decompose the graph associated to such matrix. There…
We resolve in the affirmative conjectures of Repovs and A. Skopenkov (1998), and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating maps of graphs on 2-dimensional surfaces by embeddings. Our…
We prove convergence of Goodwillie-Weiss' embedding calculus for spaces of embeddings into a manifold of dimension at most two, so in particular for diffeomorphisms between surfaces. We also relate the Johnson filtration of the mapping…
We consider the Potts model in a magnetic field on an arbitrary graph $G$. Using a formula of F. Y. Wu for the partition function $Z$ of this model as a sum over spanning subgraphs of $G$, we prove some properties of $Z$ concerning…