Related papers: Explorable families of graphs
An edge-colored directed graph is \emph{observable} if an agent that moves along its edges is able to determine his position in the graph after a sufficiently long observation of the edge colors. When the agent is able to determine his…
We study the computability and complexity of the exploration problem in a class of highly dynamic graphs: periodically varying (PV) graphs, where the edges exist only at some (unknown) times defined by the periodic movements of carriers.…
We construct infinite families of graphs that are determined by their generalized spectrum. This construction is based on new formulae for the determinant of the walk matrix of a graph. The graphs constructed here all satisfy a lower…
We consider the problem of exploration of networks, some of whose edges are faulty. A mobile agent, situated at a starting node and unaware of which edges are faulty, has to explore the connected fault-free component of this node by…
There has been significant recent interest in graph-based nearest neighbor search methods, many of which are centered on the construction of navigable graphs over high-dimensional point sets. A graph is navigable if we can successfully move…
The study of graph queries in database theory has spanned more than three decades, resulting in a multitude of proposals for graph query languages. These languages differ in the mechanisms. We can identify three main families of languages,…
The graph exploration problem requires a group of mobile robots, initially placed arbitrarily on the nodes of a graph, to work collaboratively to explore the graph such that each node is eventually visited by at least one robot. One…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
A colored graph is a directed graph in which nodes or edges have been assigned colors that are not necessarily unique. Observability problems in such graphs consider whether an agent observing the colors of edges or nodes traversed on a…
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…
We study a number of graph exploration problems in the following natural scenario: an algorithm starts exploring an undirected graph from some seed node; the algorithm, for an arbitrary node $v$ that it is aware of, can ask an oracle to…
Can we learn how to explore unknown spaces efficiently? To answer this question, we study the problem of Online Graph Exploration, the online version of the Traveling Salesperson Problem. We reformulate graph exploration as a reinforcement…
Consider an agent exploring an unknown graph in search of some goal state. As it walks around the graph, it learns the nodes and their neighbors. The agent only knows where the goal state is when it reaches it. How do we reach this goal…
Population structure can be modelled by evolutionary graphs, which can have a substantial, but very subtle influence on the fate of the arising mutants. Individuals are located on the nodes of these graphs, competing with each other to…
An oblivious mobile robot is a stateless computational entity located in a spatial universe, capable of moving in that universe. When activated, the robot observes the universe and the location of the other robots, chooses a destination,…
Recently, B\"ockenhauer, Frei, Unger, and Wehner (SIROCCO 2023) introduced a novel variant of the graph exploration problem in which a single memoryless agent must visit all nodes of an unknown, undirected, and connected graph before…
A mobile agent navigating along edges of a simple connected graph, either finite or countably infinite, has to find an inert target (treasure) hidden in one of the nodes. This task is known as treasure hunt. The agent has no a priori…
We consider the problem of human-assisted graph search: given a directed acyclic graph with some (unknown) target node(s), we consider the problem of finding the target node(s) by asking an omniscient human questions of the form "Is there a…
We investigate character degree graphs of solvable groups. In particular, we provide general results that can be used to eliminate which degree graphs can occur as solvable groups. Finally, we show a specific family of graphs cannot occur…
Graph searching is one of the simplest and most widely used tools in graph algorithms. Every graph search method is defined using some particular selection rule, and the analysis of the corresponding vertex orderings can aid greatly in…