Related papers: Compositions of Digraphs: A Survey
Deep generative models have achieved great success in areas such as image, speech, and natural language processing in the past few years. Thanks to the advances in graph-based deep learning, and in particular graph representation learning,…
We give a survey on the different results involving the topological structure of subsums of null sequences.
We prove new bijections between different variants of Dyck paths and integer compositions, which give combinatorial explanations of their simple counting formula $4^{n-1}$. These give relations between different statistics, such as the…
Polygraphs are a higher-dimensional generalization of the notion of directed graph. Based on those as unifying concept, this monograph on polygraphs revisits the theory of rewriting in the context of strict higher categories, adopting the…
Directed graphs can be partitioned in so-called passages. A passage P is a set of edges such that any two edges sharing the same initial vertex or sharing the same terminal vertex are both inside $P$ or are both outside of P. Passages were…
In this paper we discuss the connected components of underlying graphs of halving lines' configurations. We show how to create a configuration whose underlying graph is the union of two given underlying graphs. We also prove that every…
In this article, a framework for defining and analysing a family of graphs or networks from symbolic music information is discussed. Such graphs concern different types of elements, such as pitches, chords and rhythms, and the relations…
Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique…
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…
In the field of mathematics, a purely combinatorial equivalent to a simplicial complex, or more generally, a down-set, is an abstract structure known as a family of sets. This family is closed under the operation of taking subsets, meaning…
Subgraph reconfiguration is a family of problems focusing on the reachability of the solution space in which feasible solutions are subgraphs, represented either as sets of vertices or sets of edges, satisfying a prescribed graph structure…
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…
In this paper we study fundamental connectivity properties of hypergraphs from a graph-theoretic perspective, with the emphasis on cut edges, cut vertices, and blocks. To prepare the ground, we define various types of subhypergraphs, as…
We introduce succinct lossless representations of query results called covers. They are subsets of the query results that correspond to minimal edge covers in the hypergraphs of these results. We first study covers whose structures are…
Cographs--defined most simply as complete graphs with colored lines--both dualize and generalize ordinary graphs, and promise a comparably wide range of applications. This article introduces them by examples, catalogues, and elementary…
A digraph $D=(V,A)$ has a good decomposition if $A$ has two disjoint sets $A_1$ and $A_2$ such that both $(V,A_1)$ and $(V,A_2)$ are strong. Let $T$ be a digraph with $t$ vertices $u_1,\dots , u_t$ and let $H_1,\dots H_t$ be digraphs such…
This paper is simply a collection of process diagrams for further use and reference. These are diagrams about different approaches to research.
Chordal graphs are important in algorithmic graph theory. Chordal digraphs are a digraph analogue of chordal graphs and have been a subject of active studies recently. Unlike chordal graphs, chordal digraphs lack many structural properties…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.