Related papers: Semantic Limits of Dense Combinatorial Objects
Motivated by the work of Lov\'asz and Szegedy on the convergence and limits of dense graph sequences, we investigate the convergence and limits of finite trees with respect to sampling in normalized distance. Based on separable real trees,…
The theory of limits of dense graph sequences was initiated by Lovasz and Szegedy. We give a possible generalization of this theory to multigraphs. Our proofs are based on the correspondence between dense graph limits and countable,…
The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…
In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…
This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…
In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. Towards this, we proposed the concepts of class obstruction,…
We introduce and investigate generalizations of interval and proper interval graphs to simplicial complexes, including strong interval, unit interval, and under closed variants. Through equivalent combinatorial and algebraic…
We consider the problem of deriving upper bounds on the parameters of sum-rank-metric codes, with focus on their dimension and block length. The sum-rank metric is a combination of the Hamming and the rank metric, and most of the available…
In this survey, we have attempted to show some developmental milestones on the characterizations of intersection graphs of hypergraphs. The theory of intersection graphs of hypergraphs has been a classical topic in the theory of special…
We develop a notion of containment for independent sets in hypergraphs. For every $r$-uniform hypergraph $G$, we find a relatively small collection $C$ of vertex subsets, such that every independent set of $G$ is contained within a member…
Reasoning about object affordances allows an autonomous agent to perform generalised manipulation tasks among object instances. While current approaches to grasp affordance estimation are effective, they are limited to a single hypothesis.…
We explain how to see finite combinatorics of preorders implicit in the {text} of basic topological definitions or arguments in (Bourbaki, General topology, Ch.I), and define a concise combinatorial notation such that complete definitions…
We present a system for object recognition based on a semantic graph representation, which the system can learn from image examples. This graph is based on intrinsic properties of objects such as structure and geometry, so it is more robust…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
Simple methods permit to generalize the concepts of iteration and of recursive processes. We shall see briefly on several examples what these methods generate. In additive sequences, we shall encounter not only the golden or the silver…
This is a survey on the amalgamated limit, a limit construction for complete Boolean algebras in iterated forcing theory, which generalizes both the direct limit and the two-step amalgamation. We focus in particular on examples of the…
For a strongly connected category $\mathcal C$ with pair-wise coproducts, we introduce a cosimplicial object, which serves as a sort of resolution for computing higher derived functors of ${\sf lim} : \mathrm{Ab}^{\mathcal C}\to…
Based on the definition of Riemann definite integral,deleting items and disturbing mesh theorems on Riemann sums are given. After deleting some items or disturbing the mesh of partition, the limit of Riemann sums still converges to Riemann…
The aim of this paper is to generalize the notion of the coloring complex of a graph to hypergraphs. We present three different interpretations of those complexes -- a purely combinatorial one and two geometric ones. It is shown, that most…
We introduce the Density Formula for (topological) drawings of graphs in the plane or on the sphere, which relates the number of edges, vertices, crossings, and sizes of cells in the drawing. We demonstrate its capability by providing…