相关论文: Contains and Inside relationships within combinato…

Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…

Many real-world complex networks are best modeled as bipartite (or 2-mode) graphs, where nodes are divided into two sets with links connecting one side to the other. However, there is currently a lack of methods to analyze properly such…

Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…

Regular hypermaps with underlying simple hypergraphs are analysed. We obtain an algorithm to classify the regular embeddings of simple hypergraphs with given order, and determine the automorphism groups of regular embedding of simple…

This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…

The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…

Let $\Gamma$ be a connected bridgeless metric graph, and fix a point $v$ of $\Gamma$. We define combinatorial iterated integrals on $\Gamma$ along closed paths at $v$, a unipotent generalization of the usual cycle pairing and the…

Table structure recognition is a challenging task due to the various structures and complicated cell spanning relations. Previous methods handled the problem starting from elements in different granularities (rows/columns, text regions),…

A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…

Configuration space integrals are powerful tools for studying the homotopy type of the space of long embeddings in terms of a combinatorial object called a graph complex. It is unknown whether these integrals give a cochain map due to…

Although there are very algorithms for embedding graphs on unbounded grids, only few results on embedding or drawing graphs on restricted grids has been published. In this work, we consider the problem of embedding paths and cycles on grid…

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring…

Rotary maps (orientably regular maps) are highly symmetric graph embeddings on orientable surfaces. This paper classifies all rotary maps whose underlying graphs are Praeger-Xu graphs, denoted $\operatorname{C}(p,r,s)$, for any odd prime…

Configurations are necklaces with prescribed numbers of red and black beads. Among all possible configurations, the regular one plays an important role in many applications. In this paper, several aspects of regular configurations are…

Zigzags in graphs embedded in surfaces are cyclic sequences of edges whose any two consecutive edges are different, have a common vertex and belong to the same face. We investigate zigzags in randomly constructed combinatorial tetrahedral…

Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping…

Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach.…

Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…

Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge…

Let $k$ be an algebraically closed field and $\alpha$, $\beta$, $\gamma$ be partitions. An algebraic group acts on the constructible set of short exact sequences of nilpotent $k$-linear operators of Jordan types $\alpha$, $\beta$, and…