Publication

Tangles and Degenerate Tangles

Andres Jacinto Ruiz Vargas
2013
Conference Papers

Abstract

We study some variants of Conway’s thrackle conjecture. A tangle is a graph drawn in the plane such that its edges are represented by continuous arcs, and any two edges share precisely one point, which is either a common endpoint or an interior point at which the two edges are tangent to each other. These points of tangencies are assumed to be distinct. If we drop the last assumption, that is, more than two edges may touch one another at the same point, then the drawing is called a degenerate tangle. We settle a problem of Pach, Radoičić, and Tóth [7], by showing that every degenerate tangle has at most as many edges as vertices. We also give a complete characterization of tangles.

Official source

https://infoscience.epfl.ch/entities/publication/b2f87a33-c098-4e19-b8c8-23c934faaf71

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Andres Jacinto Ruiz Vargas
2013
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/b2f87a33-c098-4e19-b8c8-23c934faaf71

About this result

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

Related concepts (32)

Tangent space

In mathematics, the tangent space of a manifold is a generalization of to curves in two-dimensional space and to surfaces in three-dimensional space in higher dimensions. In the context of physics the tangent space to a manifold at a point can be viewed as the space of possible velocities for a particle moving on the manifold. In differential geometry, one can attach to every point of a differentiable manifold a tangent space—a real vector space that intuitively contains the possible directions in which one can tangentially pass through .

Graph drawing

Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics. A drawing of a graph or network diagram is a pictorial representation of the vertices and edges of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph.

Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x = c if the line passes through the point (c, f(c)) on the curve and has slope f(c), where f is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space.

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