Related papers: Arrow graphs and their focal curves

Usually, mathematical objects have highly parallel interpretations. In this paper, we consider them as sequential constructors of other objects. In particular, we prove that every reflexive directed graph can be interpreted as a program…

Given two graphs G and H, we ask under which conditions there is a relation R that generates the edges of H given the structure of graph G. This construction can be seen as a form of multihomomorphism. It generalizes surjective…

We study a three-dimensional analogue to the well-known graph visualization approach known as arc diagrams. We provide several algorithms that achieve good angular resolution for 3D arc diagrams, even for cases when the arcs must project to…

In this work we study a problem about analytic continuation along parallel algebraic curves.

The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…

The central curve of a linear program is an algebraic curve specified by linear and quadratic constraints arising from complementary slackness. It is the union of the various central paths for minimizing or maximizing the cost function over…

Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey…

We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.

In this paper we introduce arrow algebras, simple algebraic structures which induce elementary toposes through the tripos-to-topos construction. This includes localic toposes as well as various realizability toposes, in particular, those…

Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional…

We introduce a new arc in directed graphs of integers. Among other things, we determine the positive integers that have arcs to all except a finite number of positive integers. We also propose some possible research problems at the end of…

An alternative foundation for 2-categories is explored by studying graph-theoretically a partial operation on 2-cells named juncture, which can replace vertical and horizontal composition. Juncture is a generalized vertical composition of…

The projective line over a field carries structure of a groupoid with a certain correspondence between objects and arrows. We discuss to what extent the field can be reconstructed from the groupoid.

We study conchoids to algebraic curve from the perspective of algebraic geometry, analyzing their main algebraic properties. We introduce the formal definition of conchoid of an algebraic curve by means of incidence diagrams. We prove that,…

Graphs constructed to translate some graph problem into another graph problem are usually called auxiliary graphs. Specifically total graphs of simple graphs are used to translate the total colouring problem of the original graph into a…

In this article, circular arcs are considered both individually and as elements of a piecewise circular curve. The endpoint parameterization proves to be quite advantageous here. The perspective of symplectic geometry provides new vectorial…

The fine 1-curve graph of a surface is a graph whose vertices are simple closed curves on the surface and whose edges connect vertices that intersect in at most one point. We show that the automorphism group of the fine 1-curve graph is…

A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C(t) (spine curve) of its center and a radius function r(t). In this paper, we investigate when parameter curves of the canal surface are also…

A 2-factor of a graph $G$ is a 2-regular spanning subgraph of $G$. We present a survey summarising results on the structure of 2-factors in regular graphs, as achieved by various researchers in recent years.

By a {\bf generalized arc\/} we mean a continuum with exactly two non-separating points; an {\bf arc} is a metrizable generalized arc. It is well known that any two arcs are homeomorphic (to the real closed unit interval); we show that any…