Related papers: Shelling and Sinking Graphs on the Sphere
The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After…
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…
Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…
We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional $Q$-curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of…
A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with different absolute order, writes the conversion as…
We prove that every locally Hamiltonian graph with $n\ge 3$ vertices and possibly with multiple edges has at least $3n-6$ edges with equality if and only if it triangulates the sphere. As a consequence, every edge-maximal embedding of a…
We consider the problem of finding an inductive construction, based on vertex splitting, of triangulated spheres with a fixed number of additional edges (braces). We show that for any positive integer $b$ there is such an inductive…
We report experimental measurements of the translational and rotational dynamics of a large buoyant sphere in isotropic turbulence. We introduce an efficient method to simultaneously determine the position and (absolute) orientation of a…
Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to…
The monography considers the problem of constructing a Hamiltonian cycle in a complete graph. A rule for constructing a Hamiltonian cycle based on isometric cycles of a graph is established. An algorithm for constructing a Hamiltonian cycle…
To understand how spherical geometry influences the dynamics of gravity-driven subduction of oceanic lithosphere on Earth, we study a simple model of a thin and dense axisymmetric shell of thickness $h$ and viscosity $\eta_1$ sinking in a…
In this paper we show lower bounds for a certain large class of algorithms solving the Graph Isomorphism problem, even on expander graph instances. Spielman [25] shows an algorithm for isomorphism of strongly regular expander graphs that…
We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold M. Under the assumption that the sectional curvature of M is strictly positive, we prove the existence of a smoothly immersed sphere…
An extension of the Method of Regularized Stokeslets (MRS) in three dimensions is developed for triangulated surfaces with a piecewise linear force distribution. The method extends the regularized Stokeslet segment methodology used for…
If a (cusped) surface S admits an ideal triangulation T with no shears, we show an efficient algorithm to give S as a quotient of hypebolic plane by a subgroup of PSL(2, Z). The algorithm runs in time O(n log n), where n is the number of…
In the given paper the algorithm describing original and universal principles of a triangulation of a smooth molecular surface: solvent excluding solvent (SES), received by primary and secondary rolling, and solvent accessible surface (SAS)…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
We introduce a recursive procedure for computing the number of realizations of a minimally rigid graph on the sphere up to rotations. We accomplish this by combining two ingredients. The first is a framework that allows us to think of such…
The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph-minor embedding methods. These methods allow non-native problems to be adapted to the target annealer's architecture. The…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…