Related papers: Recipes for Edge-Transitive Tetravalent Graphs
In this paper, we consider the problems from the area of sublinear-time algorithms of edge sampling, edge counting, and triangle counting. Part of our contribution is that we consider three different settings, differing in the way in which…
In this paper we describe all edge-colored graphs that are fully symmetric with respect to colors and transitive on every set of edges of the same color. They correspond to fully symmetric homogeneous factorizations of complete graphs. Our…
Graph is powerful for representing various types of real-world data. The topology (edges' presence) and edges' features of a graph decides the message passing mechanism among vertices within the graph. While most existing approaches only…
The distance of a graph from being triangle-free is a fundamental graph parameter, counting the number of edges that need to be removed from a graph in order for it to become triangle-free. Its corresponding computational problem is the…
Graphs are ubiquitous and ever-present data structures that have a wide range of applications involving social networks, knowledge bases and biological interactions. The evolution of a graph in such scenarios can yield important insights…
A graph G=(V,E) is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree T and two non-negative real numbers `d' and `D' such that each leaf `u' of T is a node of V and the edge `(u,v) belongs to E' iff `d <= d_T(u, v)…
We present a edge-coloured analogue of the duality theorem for transitive tournaments and directed paths. Given a edge-coloured path $P$ whose edges alternate blue and red, we construct a edge-coloured graph $D$ so that for any…
Graph generation with Machine Learning is an open problem with applications in various research fields. In this work, we propose to cast the generative process of a graph into a sequential one, relying on a node ordering procedure. We use…
Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics, including image segmentation, shape matching, or the computation of geodesic distances on discrete surfaces. Traditionally, the concept of…
Real-world graphs often contain spatio-temporal information and evolve over time. Compared with static graphs, spatio-temporal graphs have very different characteristics, presenting more significant challenges in data volume, data velocity,…
A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in…
Theta graphs are important geometric graphs that have many applications, including wireless networking, motion planning, real-time animation, and minimum-spanning tree construction. We give closed form expressions for the average degree of…
Simple drawings are drawings of graphs in which any two edges intersect at most once (either at a common endpoint or a proper crossing), and no edge intersects itself. We analyze several characteristics of simple drawings of complete…
Recently, the deep learning community has given growing attention to neural architectures engineered to learn problems in relational domains. Convolutional Neural Networks employ parameter sharing over the image domain, tying the weights of…
Let $\mathcal{OG}(4)$ denote the family of all graph-group pairs $(\Gamma, G)$ where $\Gamma$ is finite, 4-valent, connected, and $G$-oriented ($G$-half-arc-transitive). A subfamily of $\mathcal{OG}(4)$ has recently been identified as…
A bipartite graph is called bipancyclic if it contains cycles of every even length from four up to the number of vertices in the graph. A theorem of Schmeichel and Mitchem states that for $n \geq 4$, every balanced bipartite graph on $2n$…
Graphs and networks are used to model interactions in a variety of contexts. There is a growing need to quickly assess the characteristics of a graph in order to understand its underlying structure. Some of the most useful metrics are…
Answering an open question from 2007, we construct infinite $k$-crossing-critical families of graphs that contain vertices of any prescribed odd degree, for any sufficiently large~$k$. To answer this question, we introduce several…
This paper introduces a 3D shape generative model based on deep neural networks. A new image-like (i.e., tensor) data representation for genus-zero 3D shapes is devised. It is based on the observation that complicated shapes can be well…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…