Related papers: On operations preserving semi-transitive orientabi…
Graph modification problems are computational tasks where the goal is to change an input graph $G$ using operations from a fixed set, in order to make the resulting graph satisfy a target property, which usually entails membership to a…
We give a unified approach to analysing, for each positive integer $s$, a class of finite connected graphs that contains all the distance transitive graphs as well as the locally $s$-arc transitive graphs of diameter at least $s$. A graph…
We present algorithms and experiments for the visualization of directed graphs that focus on displaying their reachability information. Our algorithms are based on the concepts of the path and channel decomposition as proposed in the…
Let $X$ be a finite vertex-transitive graph of valency $d$, and let $A$ be the full automorphism group of $X$. Then the arc-type of $X$ is defined in terms of the sizes of the orbits of the action of the stabiliser $A_v$ of a given vertex…
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…
Any graph which is not vertex transitive has a proper induced subgraph which is unique due to its structure or the way of its connection to the rest of the graph. We have called such subgraph as an anchor. Using an anchor which, in fact, is…
Transformer-based models have recently shown success in representation learning on graph-structured data beyond natural language processing and computer vision. However, the success is limited to small-scale graphs due to the drawbacks of…
A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $(x,y)$ is an edge in $E$. A graph is word-representable if and only if it is…
A (fully) dynamic graph algorithm is a data structure that supports edge insertions, edge deletions, and answers specific queries pertinent to the problem at hand. In this work, we address the fully dynamic edge orientation problem, also…
Graph modification problems are typically asked as follows: is there a small set of operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and…
Motivated by very large-scale communication networks, we newly introduce exponentiation of graphs. Using the exponential operation on graphs, we can construct various graphs of multi-exponential order with logarithmic diameter. We show that…
We study groups acting vertex-transitively on connected, trivalent graphs such that stabilizers of vertices are infinite. If the action is edge-transitive, we prove that the graph has to be a tree. We analyze the case where the action is…
Reeb graphs are widely used in a range of fields for the purposes of analyzing and comparing complex spaces via a simpler combinatorial object. Further, they are closely related to extended persistence diagrams, which largely but not…
A connected graph $\Gamma=(V,E)$ of valency at least $3$ is called a basic $2$-arc-transitive graph if its full automorphism group has a subgroup $G$ with the following properties: (i) $G$ acts transitively on the set of $2$-arcs of…
The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…
The goal of this paper is to extend the standard invariant-theoretic design, well-developed in the reductive case, to the setting of representation of certain non-reductive groups. This concerns the following notions and results: the…
Semi-supervised learning provides an effective paradigm for leveraging unlabeled data to improve a model's performance. Among the many strategies proposed, graph-based methods have shown excellent properties, in particular since they allow…
In a quest to thoroughly understand the first-order transduction hierarchy of hereditary graph classes, some questions in particular stand out; such as, what properties hold for graph classes that are first-order transductions of planar…
We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis…
Given a set $F$ of oriented graphs, a graph $G$ is an $F$-graph if it admits an $F$-free orientation. Building on previous work by Bang-Jensen and Urrutia, we propose a master algorithm that determines if a graph admits an $F$-free…