Related papers: Graph Search Trees and Their Leaves
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…
Search is an ability foundational in many important tasks, and recent studies have shown that large language models (LLMs) struggle to perform search robustly. It is unknown whether this inability is due to a lack of data, insufficient…
We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…
A tree is said to be even if for every pair of distinct leaves, the length of the unique path between them is even. In this paper we discuss the problem of determining whether an input graph has a spanning even tree. Hofmann and Walsh…
A robot finds it really hard to learn creatively and adapt to new unseen challenges. This is mainly because of the minimal information it has access to or experience towards. Paulius et al. [1] presented a way to construct functional graphs…
We consider the problem of listing all spanning trees of a graph $G$ such that successive trees differ by pivoting a single edge around a vertex. Such a listing is called a "pivot Gray code", and it has more stringent conditions than known…
A tree with at most k leaves is called k-ended tree, and a tree with exactly k leaves is called k-end tree, where a leaf is a vertex of degree one. Contraction of a graph G along the edge e means deleting the edge e and identifying its end…
A spanning tree of a network or graph is a subgraph that connects all nodes with the least number or weight of edges. The spanning tree is one of the most straightforward techniques for network simplification and sampling, and for…
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…
In phylogenetics, evolution is traditionally represented in a tree-like manner. However, phylogenetic networks can be more appropriate for representing evolutionary events such as hybridization, horizontal gene transfer, and others. In…
Over some types of trees with a given number of vertices, which trees minimize or maximize the total number of subtrees or leaf containing subtrees are studied. Here are some of the main results:\ (1)\, Sharp upper bound on the total number…
The search is based on the preliminary transformation of matrices or adjacency lists traditionally used in the study of graphs into projections cleared of redundant information (refined) followed by the selection of the desired shortest…
An out-branching of a directed graph is a rooted spanning tree with all arcs directed outwards from the root. We consider the problem of deciding whether a given directed graph D has an out-branching with at least k leaves (Directed…
The treedepth of a graph $G$ is the least possible depth of an elimination forest of $G$: a rooted forest on the same vertex set where every pair of vertices adjacent in $G$ is bound by the ancestor/descendant relation. We propose an…
This chapter studies the problem of traversing large graphs using the breadth-first search order on distributed-memory supercomputers. We consider both the traditional level-synchronous top-down algorithm as well as the recently discovered…
We investigate the searchability of complex systems in terms of their interconnectedness. Associating searchability with the number and size of branch points along the paths between the nodes, we find that scale-free networks are relatively…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
A suffix tree is able to efficiently locate a pattern in an indexed string, but not in general the most recent copy of the pattern in an online stream, which is desirable in some applications. We study the most general version of the…
The goal of graph inference is to design algorithms for learning properties of a hidden graph using queries to an oracle that returns information about the graph. Graph reconstruction, verification, and property testing are all types of…
We study vertex-ordering problems in loop-free digraphs subject to constraints on the left-going arcs, focusing on existence conditions and computational complexity. As an intriguing special case, we explore vertex-specific lower and upper…