Related papers: Isotemporal classes of n-gons
The problem of learning or reconstructing an unknown graph from a known family via partial-information queries arises as a mathematical model in various contexts. The most basic type of access to the graph is via \emph{edge queries}, where…
A graph class is monotone if it is closed under taking subgraphs. It is known that a monotone class defined by finitely many obstructions has bounded treewidth if and only if one of the obstructions is a so-called tripod, that is, a…
Graph isomorphism problem is a known hard problem. In this paper, a novel randomized algorithm is proposed for this problem which is very simple and fast. It solves the graph isomorphism problem with running time O(n^2.373) for any pair of…
An explicit algorithm is presented for testing whether two non-directed graphs are isomorphic or not. It is shown that for a graph of n vertices, the number of n independent operations needed for the test is polynomial in n. A proof that…
Graph neural networks (GNNs) for temporal graphs have recently attracted increasing attentions, where a common assumption is that the class set for nodes is closed. However, in real-world scenarios, it often faces the open set problem with…
In a temporal graph the edge set dynamically changes over time according to a set of time-labels associated with each edge that indicates at which time-steps the edge is available. Two vertices are connected if there is a path connecting…
A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a…
Hallucinations can be produced by conversational AI systems, particularly in multi-turn conversations where context changes and contradictions may eventually surface. By representing the entire conversation as a temporal graph, we present a…
In this paper, we reveal an intriguing relationship between two seemingly unrelated notions: letter graphs and geometric grid classes of permutations. An important property common for both of them is well-quasi-orderability, implying, in a…
Deep learning models have achieved huge success in numerous fields, such as computer vision and natural language processing. However, unlike such fields, it is hard to apply traditional deep learning models on the graph data due to the…
Most instruments - formalisms, concepts, and metrics - for social networks analysis fail to capture their dynamics. Typical systems exhibit different scales of dynamics, ranging from the fine-grain dynamics of interactions (which recently…
A temporal (directed) graph is a graph whose edges are available only at specific times during its lifetime, $\tau$. Paths are sequences of adjacent edges whose appearing times are either strictly increasing or non-strictly increasingly…
Given a graph $G$, the graph $[G]$ obtained by adding, for each pair of vertices of $G$, a unique vertex adjacent to both vertices is called the binding graph of $G$. In this work, we show that the class of binding graphs is…
Motifs are thought to be some fundamental components of social face-to-face interaction temporal networks. However, the motifs previously considered are either limited to a handful of nodes and edges, or do not include triangles, which are…
We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
A graph is said to be edge-transitive if its automorphism group acts transitively on its edges. It is known that edge-transitive graphs are either vertex-transitive or bipartite. In this paper we present a complete classification of all…
In recent work, Rosenbaum and Wagner showed that isomorphism of explicitly listed $p$-groups of order $n$ could be tested in $n^{\frac{1}{2}\log_p n + O(p)}$ time, roughly a square root of the classical bound. The $O(p)$ term is entirely…
In social networks the {\sc Strong Triadic Closure} is an assignment of the edges with strong or weak labels such that any two vertices that have a common neighbor with a strong edge are adjacent. The problem of maximizing the number of…
We study the problem of finding an Euler tour in an undirected graph G in the W-Streaming model with O(n polylog(n)) RAM, where n resp. m is the number of nodes resp. edges of G. Our main result is the first one pass W-Streaming algorithm…