Related papers: Algorithmic Traversals of Infinite Graphs
For some geometric graph classes, tractability of testing first-order formulas is precisely characterised by the graph parameter twin-width. This was first proved for interval graphs among others in [BCKKLT, IPEC '22], where the equivalence…
Graphlet analysis is an approach to network analysis that is particularly popular in bioinformatics. We show how to set up a system of linear equations that relate the orbit counts and can be used in an algorithm that is significantly…
We extend to infinite graphs the matroidal characterization of finite graph duality, that two graphs are dual iff they have complementary spanning trees in some common edge set. The naive infinite analogue of this fails. The key in an…
Graph traversals are a basic but fundamental ingredient for a variety of graph algorithms and graph-oriented queries. To achieve the best possible query performance, they need to be implemented at the core of a database management system…
Graph exploration is one of the fundamental tasks performed by a mobile agent in a graph. An $n$-node graph has unlabeled nodes, and all ports at any node of degree $d$ are arbitrarily numbered $0,\dots, d-1$. A mobile agent, initially…
Traversals are commonly seen in tree data structures, and performance-enhancing transformations between tree traversals are critical for many applications. Existing approaches to reasoning about tree traversals and their transformations are…
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrary planar graph to index the decomposition. We prove that…
The last in-tree recognition problem asks whether a given spanning tree can be derived by connecting each vertex with its rightmost left neighbor of some search ordering. In this study, we demonstrate that the last-in-tree recognition…
We propose a novel sequence prediction method for sequential data capturing node traversals in graphs. Our method builds on a statistical modelling framework that combines multiple higher-order network models into a single multi-order…
Let $G$ be an $n$-vertex connected graph. A cyclic base ordering of $G$ is a cyclic ordering of all edges such that every cyclically consecutive $n-1$ edges induce a spanning tree of $G$. In this project, we study cyclic base ordering of…
The Breadth First Search (BFS) algorithm is the foundation and building block of many higher graph-based operations such as spanning trees, shortest paths and betweenness centrality. The importance of this algorithm increases each day due…
The Burling sequence is a sequence of triangle-free graphs of increasing chromatic number. Any graph which is an induced subgraph of a graph in this sequence is called a Burling graph. These graphs have attracted some attention because they…
A transitive graph is 2-dimensional if it can be represented as the intersection of two linear orders. Such representations make answering of reachability queries trivial, and allow many problems that are NP-hard on arbitrary graphs to be…
This work analyzes Graph Neural Networks, a generalization of Fully-Connected Deep Neural Nets on Graph structured data, when their width, that is the number of nodes in each fullyconnected layer is increasing to infinity. Infinite Width…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of…
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…
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which…
The Pathwidth Theorem states that if a class of graphs has unbounded pathwidth, then it contains all trees as graph minors. We prove a similar result for dense graphs. More precisely, we give a finite family of tree-like patterns and prove…
(First-order) transductions are a basic notion capturing graph modifications that can be described in first-order logic. In this work, we propose an efficient algorithmic method to approximately reverse the application of a transduction,…
Algorithms for laying out large graphs have seen significant progress in the past decade. However, browsing large graphs remains a challenge. Rendering thousands of graphical elements at once often results in a cluttered image, and…