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A directed graph $D$ is singly connected if for every ordered pair of vertices $(s,t)$, there is at most one path from $s$ to $t$ in $D$. Graph orientation problems ask, given an undirected graph $G$, to find an orientation of the edges…
Given a graph $G$ with a terminal set $R \subseteq V(G)$, the Steiner tree problem (STREE) asks for a set $S\subseteq V(G) \setminus R$ such that the graph induced on $S\cup R$ is connected. A split graph is a graph which can be partitioned…
Polypeptides can self-assemble into hierarchically organized fibrils consisting of a stack of individually folded polypeptides driven together by hydrophobic interaction. Using a coarse grained model, we systematically studied this…
We propose an alternative proof concerning necessary and sufficient conditions to split the problem of searching for d-separators and building the skeleton of a DAG into small problems for every node of a separation tree T. The proof is…
For a graph $G$ on $n$ vertices, naively sampling the position of a random walk of at time $t$ requires work $\Omega(t)$. We desire local access algorithms supporting $\text{position}(G,s,t)$ queries, which return the position of a random…
Node embeddings are a paradigm in non-parametric graph representation learning, where graph nodes are embedded into a given vector space to enable downstream processing. State-of-the-art node-embedding algorithms, such as DeepWalk and…
Single-molecule break junction measurements deliver a huge number of conductance vs.\ electrode separation traces. Along such measurements the target molecules may bind to the electrodes in different geometries, and the evolution and…
The influence of substrate steps on the bottom-up synthesis of atomically precise graphene nanoribbons (GNRs) on an Au(111) surface is investigated. A straight surface step is found to promote the assembly of long and compact arrays of…
In this paper, we analyze the dynamics of quantum walks on a graph structure resulting from the integration of a main connected graph $G$ and a secondary connected graph $G'$. This composite graph is formed by a disjoint union of $G$ and…
Let $D$ be a digraph. A subset $S$ of $V(D)$ is a stable set if every pair of vertices in $S$ is non-adjacent in $D$. A collection of disjoint paths $\mathcal{P}$ of $D$ is a path partition of $V(D)$, if every vertex in $V(D)$ is exactly on…
Let $P$ be a set of $n$ points in $\mathbb{R}^d$, and let $\varepsilon,\psi \in (0,1)$ be parameters. Here, we consider the task of constructing a $(1+\varepsilon)$-spanner for $P$, where every edge might fail (independently) with…
The rotor-router model, also called the Propp machine, was introduced as a deterministic alternative to the random walk. In this model, a group of identical tokens are initially placed at nodes of the graph. Each node maintains a cyclic…
We propose a deep neural network fusion architecture for fast and robust pedestrian detection. The proposed network fusion architecture allows for parallel processing of multiple networks for speed. A single shot deep convolutional network…
We study the polyhedral properties of three problems of constructing an optimal complete bipartite subgraph (a biclique) in a bipartite graph. In the first problem we consider a balanced biclique with the same number of vertices in both…
Given an input graph G and a node v in G, homogeneous network embedding (HNE) maps the graph structure in the vicinity of v to a compact, fixed-dimensional feature vector. This paper focuses on HNE for massive graphs, e.g., with billions of…
Exercising direct control over the unusual electronic structures arising from quantum confinement effects in graphene nanoribbons (GNRs) - atomically defined quasi one-dimensional (1D) strips of graphene - is intimately linked to geometric…
The simplest way to make a dynamical system out of a finite connected graph $G$ is to give it a polarization, that is to say a cyclic ordering of the edges incident to a vertex, for each vertex. The phase space $\mathcal{P}(G)$ then…
The reassembling of a simple connected graph G = (V,E) is an abstraction of a problem arising in earlier studies of network analysis. The reassembling process has a simple formulation (there are several equivalent formulations) relative to…
A graph covering projection, also referred to as a locally bijective homomorphism, is a mapping between the vertices and edges of two graphs that preserves incidences and is a local bijection. This concept originates in topological graph…
Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…