Related papers: Characterization of signed Gauss paragraphs

We consider surfaces embedded in a Riemannian manifold of arbitrary dimension and prove that many aspects of their differential geometry can be expressed in terms of a Poisson algebraic structure on the space of smooth functions of the…

This paper concerns the global theory of properly embedded spacelike surfaces in three-dimensional Minkowski space in relation to their Gaussian curvature. We prove that every regular domain which is not a wedge is uniquely foliated by…

Let $G$ be a graph and $T$ be a vertex subset of $G$ with even cardinality. A $T$-join of $G$ is a subset $J$ of edges such that a vertex of $G$ is incident with an odd number of edges in $J$ if and only if the vertex belongs to $T$.…

In this paper, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets. Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks…

A family $\mathcal{P}$ of subgraphs of $G$ is called a {\it path cover} (resp. a {\it path partition}) of $G$ if $\bigcup _{P\in \mathcal{P}}V(P)=V(G)$ (resp. $\dot\bigcup _{P\in \mathcal{P}}V(P)=V(G)$) and every element of $\mathcal{P}$ is…

We investigate two optimization problems on area-proportional rectangle contact representations for layered, embedded planar graphs. The vertices are represented as interior-disjoint unit-height rectangles of prescribed widths, grouped in…

In this work we prove the existence of embedded closed minimal hypersurfaces in non-compact manifolds containing a bounded open subset with smooth and strictly mean-concave boundary and a natural behavior on the geometry at infinity. For…

A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…

Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general…

Let $G$ be a Cayley graph of the elementary abelian $2$-group $\mathbb{Z}_2^{n}$ with respect to a set $S$ of size $d$. We prove that for any such $G, S$ and $d$, the maximum degree of any induced subgraph of $G$ on any set of more than…

We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…

A translation surface of Euclidean space $\r^3$ is the sum of two regular curves $\alpha$ and $\beta$, called the generating curves. In this paper we classify the minimal translation surfaces of $\r^3$ and we give a method of construction…

Given a semisimple Lie algebra $\mathfrak{g}$, we can represent invariants of tensor products of fundamental representations of the quantum enveloping algebra $U_q(\mathfrak{g})$ using particular directed graphs called webs. In particular…

A Gauss diagram (or, more generally, a chord diagram) consists of a circle and some chords inside it. Gauss diagrams are a well-established tool in the study of topology of knots and of planar and spherical curves. Not every Gauss diagram…

Embedded minimal surfaces of finite total curvature in $\mathbb{R}^3$ are reasonably well understood: From far away, they look like intersecting catenoids and planes, suitably desingularized. We consider the larger class of harmonic…

We show that min-max minimal hypersurfaces can be localized. As a consequence, we obtain the sharp generalization to complete manifolds of the famous Almgren-Pitts min-max theorem in closed manifolds. We use this result to prove the…

A recent result of Chepoi, Estellon and Vaxes [DCG '07] states that any planar graph of diameter at most 2R can be covered by a constant number of balls of size R; put another way, there are a constant-sized subset of vertices within which…

Graph embedding methods transform high-dimensional and complex graph contents into low-dimensional representations. They are useful for a wide range of graph analysis tasks including link prediction, node classification, recommendation and…

In this paper, we study the Cartesian product of signed graphs as defined by Germina, Hameed and Zaslavsky (2011). Here we focus on its algebraic properties and look at the chromatic number of some Cartesian products. One of our main…

We study representations of the classical infinite dimensional real simple Lie groups $G$ induced from factor representations of minimal parabolic subgroups $P$. This makes strong use of the recently developed structure theory for those…