Related papers: Separations of sets
This article provides structural characterization of simple graphs whose edge-set can be partitioned into maximum matchings. We use Vizing's classification of simple graphs based on edge chromatic index.
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
The Explainable Abstract Trains Dataset is an image dataset containing simplified representations of trains. It aims to provide a platform for the application and research of algorithms for justification and explanation extraction. The…
Bipartite graphs model the relationship between two disjoint sets of objects. They have a wide range of applications and are often visualized as a 2-layered drawing, where each set of objects is visualized as a set of vertices (points) on…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
Graph covers are a way to describe continuous maps (and homeomorphisms) of a Cantor set, more generally than e.g.\ Bratteli-Vershik systems. Every continuous map on a zero-dimensional compact set can be expressed by a graph cover (e.g.\…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
Heap data is potentially unbounded and seemingly arbitrary. As a consequence, unlike stack and static memory, heap memory cannot be abstracted directly in terms of a fixed set of source variable names appearing in the program being…
We define a partition of a reductive group into finitely many subsets, refining the partition of the group into strata. We state some conjectural properties of these subsets (called substrata) and verify them in some examples.
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
Automated synthesis of reactive control protocols from temporal logic specifications has recently attracted considerable attention in various applications in, for example, robotic motion planning, network management, and hardware design. An…
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…
Alternative set theory (AST) may be suitable for the ones who try to capture objects or phenomenons with some kind of indefiniteness of a border. While AST provides various notions for advanced mathematical studies, correspondence of them…
The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
One perspective on tree decompositions is that they display (low-order) separations of the underlying graph or matroid. The separations displayed by a tree decomposition are necessarily nested. In 2013, Clark and Whittle proved the…
This thesis (defended 10/07/2019) develops a theory of networks of hybrid open systems and morphisms. It builds upon a framework of networks of continuous-time open systems as product and interconnection. We work out categorical notions for…
Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…
The paper develops an abstract (over-approximating) semantics for double-pushout rewriting of graphs and graph-like objects. The focus is on the so-called materialization of left-hand sides from abstract graphs, a central concept in…