Related papers: Counting unrooted maps using tree-decomposition

In this paper, we give a decomposition of triply rooted trees into three doubly rooted trees. This leads to a combinatorial interpretation of an identity conjectured by Lacasse in the study of the PAC-Bayesian machine learning theory, and…

We give a recursion formula to generate all equivalence classes of biconnected graphs with coefficients given by the inverses of the orders of their groups of automorphisms. We give a linear map to produce a connected graph with say, u,…

The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…

We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many…

Spectrum cartography aims at estimating power propagation patterns over a geographical region across multiple frequency bands (i.e., a radio map)---from limited samples taken sparsely over the region. Classic cartography methods are mostly…

Multiresolution decomposition is commonly understood as a procedure to capture scale-dependent features in random signals. Such methods were first established for image processing and typically rely on raster or regularly gridded data. In…

We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal…

The canonical tree-decomposition theorem, given by Robertson and Seymour in their seminal graph minors series, turns out to be one of the most important tool in structural and algorithmic graph theory. In this paper, we provide the…

The classical notion of retraction map used to approximate geodesics is extended and rigorously defined to become a powerful tool to construct geometric integrators and it is called discretization map. Using the geometry of the tangent and…

We present a construction method for triharmonic maps to spheres. In particular, we show that for any $m\in\mathbb{N}$ with $m\geq 3$ there exists a triharmonic map from $\mathbb{R}^m\setminus\{0\}$ into a round sphere. In addition, we…

Decomposing an algebraic variety into irreducible or equidimensional components is a fundamental task in classical algebraic geometry and has various applications in modern geometry engineering. Several researchers studied the problem and…

Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…

Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…

Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…

Hypertree decompositions of hypergraphs are a generalization of tree decompositions of graphs. The corresponding hypertree-width is a measure for the cyclicity and therefore tractability of the encoded computation problem. Many NP-hard…

Let $P$ be a set of $n$ points in general position on the plane. A set of closed convex polygons with vertices in $P$, and with pairwise disjoint interiors is called a convex decomposition of $P$ if their union is the convex hull of $P$,…

Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…

In recent years many algorithms have been developed for finding patterns in graphs and networks. A disadvantage of these algorithms is that they use subgraph isomorphism to determine the support of a graph pattern; subgraph isomorphism is a…

We combine two methods for the lossless compression of unlabeled graphs - entropy compressing adjacency lists and computing canonical names for vertices - and solve an ensuing novel optimisation problem: Minimum-Entropy Tree-Extraction…

A metric phylogenetic tree relating a collection of taxa induces weighted rooted triples and weighted quartets for all subsets of three and four taxa, respectively. New intertaxon distances are defined that can be calculated from these…