Related papers: K\"{o}nigsberg Sightseeing: Eulerian Walks in Temp…
Given an undirected graph $G$, the problem of deciding whether $G$ admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (G\"obel et al., 1991). In this article, we relax this problem and ask…
Leonhard Euler was working for the St. Petersburg Academy of Sciences (Russia) and Prussian Academy of Sciences during various periods of his life. It is not a popular knowledge about Euler's contacts with Polish scientists of his era and…
We show that the expected time for a random walk on a (multi-)graph $G$ to traverse all $m$ edges of $G$, and return to its starting point, is at most $2m^2$; if each edge must be traversed in both directions, the bound is $3m^2$. Both…
Many applications in graph theory are motivated by routing or flow problems. Among these problems is Steiner Orientation: given a mixed graph G (having directed and undirected edges) and a set T of k terminal pairs in G, is there an…
We show that the graph transformation problem of turning a simple graph into an Eulerian one by a minimum number of single edge switches is NP-hard. Further, we show that any simple Eulerian graph can be transformed into any other such…
Pedestrian trajectory prediction aims to forecast future movements based on historical paths. Spatial-temporal (ST) methods often separately model spatial interactions among pedestrians and temporal dependencies of individuals. They…
We examine the problem of maximizing the reachability of a given source in temporal graphs that are given as the union of k temporal paths, i.e., every given path is a sequence of edges with strictly increasing labels that denote…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. A connected graph is Eulerian if its vertex degrees are all even. In [Gutman, Cruz, Rada, Wiener index of Eulerian Graphs, Discrete…
In this paper, we prove that, given a clique-width $k$-expression of an $n$-vertex graph, \textsc{Hamiltonian Cycle} can be solved in time $n^{\mathcal{O}(k)}$. This improves the naive algorithm that runs in time $n^{\mathcal{O}(k^2)}$ by…
Temporal graphs are graphs whose edges are only present at certain points in time. Reachability in these graphs relies on temporal paths, where edges are traversed chronologically. A temporal graph that offers all-pairs reachability is said…
We define a general model of stochastically-evolving graphs, namely the \emph{Edge-Uniform Stochastically-Evolving Graphs}. In this model, each possible edge of an underlying general static graph evolves independently being either alive or…
Simultaneous Geometric Embedding (SGE) asks whether, for a given collection of graphs on the same vertex set V, there is an embedding of V in the plane that admits a crossing-free drawing with straightline edges for each of the given…
Computing paths in graph structures is a fundamental operation in a wide range of applications, from transportation networks to data analysis. The beer path problem, which captures the option of visiting points of interest, such as gas…
We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…
We apply the Euler tour technique to find subtrees of specified weight as follows. Let $k, g, N_1, N_2 \in \mathbb{N}$ such that $1 \leq k \leq N_2$, $g + h > 2$ and $2k - 4g - h + 3 \leq N_2 \leq 2k + g + h - 2$, where $h := 2N_1 - N_2$.…
This paper formalises the Canadian Traveller problem as a positional two-player game on graphs. We consider two variants depending on whether an edge is blocked. In the locally-informed variant, the traveller learns if an edge is blocked…
An important characteristic of temporal graphs is how the directed arrow of time influences their causal topology, i.e., which nodes can possibly influence each other causally via time-respecting paths. The resulting patterns are often…
Given a simple graph $G$, its line graph, denoted by $L(G)$, is obtained by representing each edge of $G$ as a vertex, with two vertices in $L(G)$ adjacent whenever the corresponding edges in $G$ share a common endpoint. By applying the…
We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…