Related papers: Mengerian graphs: characterization and recognition
Coarse graph theory concerns finding 'coarse' analogues of graph theory theorems, replacing disjointness with being far apart. One of the most interesting open questions is to find a coarse analogue of Menger's theorem, which characterizes…
The independent set on a graph $G=(V,E)$ is a subset of $V$ such that no two vertices in the subset have an edge between them. The MIS problem on $G$ seeks to identify an independent set with maximum cardinality, i.e. maximum independent…
For an undirected, simple, finite, connected graph $G$, we denote by $V(G)$ and $E(G)$ the sets of its vertices and edges, respectively. A function $\varphi:E(G)\rightarrow \{1,...,t\}$ is called a proper edge $t$-coloring of a graph $G$,…
An edge-coloring of a graph $G$ with colors $1,\ldots,t$ is called an \emph{interval $t$-coloring} if all colors are used and the colors of edges incident to each vertex of $G$ are distinct and form an interval of integers. In 1990,…
Temporal graph networks (TGNs) have gained prominence as models for embedding dynamic interactions, but little is known about their theoretical underpinnings. We establish fundamental results about the representational power and limits of…
We study how we can accelerate the spreading of information in temporal graphs via shifting operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a…
This paper endeavors to learn time-varying graphs by using structured temporal priors that assume underlying relations between arbitrary two graphs in the graph sequence. Different from many existing chain structure based methods in which…
We study the kernelization of exploration problems on temporal graphs. A temporal graph consists of a finite sequence of snapshot graphs $\mathcal{G}=(G_1, G_2, \dots, G_L)$ that share a common vertex set but might have different edge sets.…
Spatiotemporal graph represents a crucial data structure where the nodes and edges are embedded in a geometric space and can evolve dynamically over time. Nowadays, spatiotemporal graph data is becoming increasingly popular and important,…
The classical Menger's theorem states that in any undirected (or directed) graph $G$, given a pair of vertices $s$ and $t$, the maximum number of vertex (edge) disjoint paths is equal to the minimum number of vertices (edges) needed to…
Despite great success has been achieved in activity analysis, it still has many challenges. Most existing work in activity recognition pay more attention to design efficient architecture or video sampling strategy. However, due to the…
A divisor graph $G$ is an ordered pair $(V, E)$ where $V \subset \mathbbm{Z}$ and for all $u \neq v \in V$, $u v \in E$ if and only if $u \mid v$ or $v \mid u$. A graph which is isomorphic to a divisor graph is also called a divisor graph.…
Transaction graphs, which represent financial and trade transactions between entities such as bank accounts and companies, can reveal patterns indicative of financial crimes like money laundering and fraud. However, effective detection of…
Temporal graphs have become an essential tool for analyzing complex dynamic systems with multiple agents. Detecting anomalies in temporal graphs is crucial for various applications, including identifying emerging trends, monitoring network…
We study the problem of drawing a dynamic graph, where each vertex appears in the graph at a certain time and remains in the graph for a fixed amount of time, called the window size. This defines a graph story, i.e., a sequence of…
The subdivision graph $S(\Sigma)$ of a connected graph $\Sigma$ is constructed by adding a vertex in the middle of each edge. In a previous paper written with Cheryl E. Praeger, we characterised the graphs $\Sigma$ such that $S(\Sigma)$ is…
Logistics and transportation networks require a large amount of resources to realize necessary connections between locations and minimizing these resources is a vital aspect of planning research. Since such networks have dynamic connections…
Temporal Graph Neural Networks (TGNNs) aim to capture the evolving structure and timing of interactions in dynamic graphs. Although many models incorporate time through encodings or architectural design, they often compute attention over…
Connectivity in temporal graphs relies on the notion of temporal paths, in which edges follow a chronological order (either strict or non-strict). In this work, we investigate the question of how to make a temporal graph connected. More…
If the vertices composing a network interact at distinct time points, the temporal ordering of these interactions and the network's graph structure are sufficient to convey the routes by which information can flow in the network. Two…