Related papers: Unary Automatic Graphs: An Algorithmic Perspective
Graph databases in many applications---semantic web, transport or biological networks among others---are not only large, but also frequently modified. Evaluating graph queries in this dynamic context is a challenging task, as those queries…
Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning…
Graph-based modeling plays a fundamental role in many areas of computer science. In this paper, we introduce systems of graph formulas with variables for specifying graph properties; this notion generalizes the graph formulas introduced in…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
Assume that $G$ is a finite group. For every $a, b \in\mathbb N,$ we define a graph $\Gamma_{a,b}(G)$ whose vertices correspond to the elements of $G^a\cup G^b$ and in which two tuples $(x_1,\dots,x_a)$ and $(y_1,\dots,y_b)$ are adjacent if…
A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree. Weights can be positive, nonnegative or arbitrary as soon as the regularization degree is not null. Positive and nonnegative…
In the following pages we discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata. We have divided our paper into seven parts which are more or less self-contained. Needless…
Given a finite directed graph, a coloring of its edges turns the graph into a finite-state automaton. A k-synchronizing word of a deterministic automaton is a word in the alphabet of colors at its edges that maps the state set of the…
Over all graphs (or unicyclic graphs) of a given order, we characterise those graphs that minimise or maximise the number of connected induced subgraphs. For each of these classes, we find that the graphs that minimise the number of…
We consider the problem of finding a subgraph of a given graph minimizing the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already for bipartite graphs when the functions are convex on…
One of the hot topics in machine learning is the field of GNN. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph…
Assume that there is a free group action of automorphisms on a bipartite graph. If there is a perfect matching on the factor graph, then obviously there is a perfect matching on the graph. Surprisingly, the reversed is also true for…
Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…
We focus on the algorithm underlying the main result of [A. Mestre, R. Oeckl, Generating loop graphs via Hopf algebra in quantum field theory. J. Math. Phys., 47, 122302, 2006]. This is an algebraic formula to generate all connected graphs…
In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks…
The present paper is concerned with the concept of the one-way quantum computer, beyond binary-systems, and its relation to the concept of stabilizer quantum codes. This relation is exploited to analyze a particular class of quantum…
We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant degree regular graphs. We show that for $r$-regular graphs with $n$ nodes and girth at least $g$, the…
We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization…
The question whether there exists a hypergraph whose degrees are equal to a given sequence of integers is a well-known reconstruction problem in graph theory, which is motivated by discrete tomography. In this paper we approach the problem…
We present an algebraic algorithm to detect the existence of and to list all indecomposable even circuits in a given graph. We also discuss an application of our work to the study of directed cycles in digraphs.