Related papers: Truncation symmetry type graphs
Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C_n while keeping at…
We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An…
Computing spherical harmonic decompositions is a ubiquitous technique that arises in a wide variety of disciplines and a large number of scientific codes. Because spherical harmonics are defined by integrals over spheres, however, one must…
A k-outerplanar graph is a graph that can be drawn in the plane without crossing such that after k-fold removal of the vertices on the outer-face there are no vertices left. In this paper, we study how to triangulate a k-outerplanar graph…
Every finite graph admits a \emph{simple (topological) drawing}, that is, a drawing where every pair of edges intersects in at most one point. However, in combination with other restrictions simple drawings do not universally exist. For…
A zigzag in a map (a $2$-cell embedding of a connected graph in a connected closed $2$-dimensional surface) is a cyclic sequence of edges satisfying the following conditions: 1) any two consecutive edges lie on the same face and have a…
We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give…
We consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, K(k[x_1, ..., x_n]/(x_1^a_1, ..., x_n^a_n)). This naturally leads to a new generalization of the big Witt vectors. If k is a perfect field…
Let $(\Sigma,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph…
A map is a partition of the sphere into regions that are labeled as countries or holes. The vertices of a map graph are the countries of a map. There is an edge if and only if the countries are adjacent and meet in at least one point. For a…
A knotted surface in the 4-sphere may be described by means of a hyperbolic diagram that captures the 0-section of a special Morse function, called a hyperbolic decomposition. We show that every hyperbolic decomposition of a knotted surface…
We initiate the algorithmic study of retracting a graph into a cycle in the graph, which seeks a mapping of the graph vertices to the cycle vertices, so as to minimize the maximum stretch of any edge, subject to the constraint that the…
The deep diagonal map $T_k$ acts on planar polygons by connecting the $k$-th diagonals and intersecting them successively. The map $T_2$ is the pentagram map, and $T_k$ is a generalization. We study the action of $T_k$ on two subsets of the…
In \cite{CMW19}, the authors introduced $k$-entanglement breaking linear maps to understand the entanglement breaking property of completely positive maps on taking composition. In this article, we do a systematic study of $k$-entanglement…
In the first half of this article, we review the Steinberg theory for double flag varieties for symmetric pairs. For a special case of the symmetric space of type AIII, we will consider $ X = GL_{2n}/P_{(n,n)} \times GL_n / B_n^+ \times…
A simple topological graph $G$ is a graph drawn in the plane so that any pair of edges have at most one point in common, which is either an endpoint or a proper crossing. $G$ is called saturated if no further edge can be added without…
In this paper we discuss an operation on halving edges graph that we call fission. Fission replaces each point in a given configuration with a small cluster of k points. The operation interacts nicely with halving edges, so we examine its…
We consider a the minimum k-way cut problem for unweighted graphs with a size bound s on the number of cut edges allowed. Thus we seek to remove as few edges as possible so as to split a graph into k components, or report that this requires…
Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in…
A graph is called a $k$-planar unit distance graph if it can be drawn in the plane such that every edge is a unit line segment and is involved in at most $k$ crossings. We investigate $u_k(n)$, the maximum number of edges of such graphs on…