Related papers: Tangle structure trees
We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. The global structure of the graph, as…
Let $T$ be a tree, we show that the null space of the adjacency matrix of $T$ has relevant information about the structure of $T$. We introduce the Null Decomposition of trees, and use it in order to get formulas for independence number and…
Safety-critical infrastructures must operate in a safe and reliable way. Fault tree analysis is a widespread method used for risk assessment of these systems: fault trees (FTs) are required by, e.g., the Federal Aviation Administration and…
Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…
Tree-width is an invaluable tool for computational problems on graphs. But often one would like to compute on other kinds of objects (e.g. decorated graphs or even algebraic structures) where there is no known tree-width analogue. Here we…
When dealing with tabular data, models based on decision trees are a popular choice due to their high accuracy on these data types, their ease of application, and explainability properties. However, when it comes to graph-structured data,…
Attempting to recognize a tree inside a phylogenetic network is a fundamental undertaking in evolutionary analysis. In the last few years, therefore, tree-based phylogenetic networks, which are defined by a spanning tree called a…
A $k$-block in a graph $G$ is a maximal set of at least $k$ vertices no two of which can be separated in $G$ by removing less than $k$ vertices. It is separable if there exists a tree-decomposition of adhesion less than $k$ of $G$ in which…
Tangent categories provide an axiomatic framework for understanding various tangent bundles and differential operations that occur in differential geometry, algebraic geometry, abstract homotopy theory, and computer science. Previous work…
Homomorphism duality pairs play crucial role in the theory of relational structures and in the Constraint Satisfaction Problem. The case where both classes are finite is fully characterized. The case when both side are infinite seems to be…
Long document classification presents challenges in capturing both local and global dependencies due to their extensive content and complex structure. Existing methods often struggle with token limits and fail to adequately model…
This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data. These tools can be used to detect outliers and clusters. Both our prediction bands and clustering trees…
Thin spanning trees lie at the intersection of graph theory, approximation algorithms, and combinatorial optimization. They are central to the long-standing \emph{thin tree conjecture}, which asks whether every $k$-edge-connected graph…
Modern order and lattice theory provides convenient mathematical tools for pattern mining, in particular for condensed irredundant representations of pattern spaces and their efficient generation. Formal Concept Analysis (FCA) offers a…
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…
There are numerous emerging applications for digitizing trees using terrestrial and aerial laser scanning, particularly in the fields of agriculture and forestry. Interpretation of LiDAR point clouds is increasingly relying on data-driven…
During the past decades significant efforts have been made to propose data structures for answering connectivity queries on fully dynamic graphs, i.e., graphs with frequent insertions and deletions of edges. However, a comprehensive…
We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str$_0$-trees (the reduct of str-trees that forgets…
Tangent category theory is a well-established categorical framework for differential geometry. A long list of fundamental geometric constructions, such as the tangent bundle functor, vector fields, Euclidean spaces, and vector bundles have…
We introduce and study the {\em orderly spanning trees} of plane graphs. This algorithmic tool generalizes {\em canonical orderings}, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning…