Related papers: Generation of Delaney-Dress graphs
A construction described by the current author in 2017 uses two linear `prototype' graphs to build a compound graph with Ramsey properties inherited from the prototypes. This paper describes a generalisation of that construction which has…
The social graphs synthesized by the generative models are increasingly in demand due to data scarcity and concerns over user privacy. One of the key performance criteria for generating social networks is the fidelity to specified…
Graph generation is one of the most challenging tasks in recent years, and its core is to learn the ground truth distribution hiding in the training data. However, training data may not be available due to security concerns or unaffordable…
In this paper, we show the existence of a polynomial time graph isomorphism algorithm for all graphs excluding graphs that are locally trianglefree. This particular class of graphs allows to divide the graph into neighbourhood sub-graph…
We describe a procedure for the generation of functional digraphs up to isomorphism; these are digraphs with uniform outdegree 1, also called mapping patterns, finite endofunctions, or finite discrete-time dynamical systems. This procedure…
Data-driven generative modeling has made remarkable progress by leveraging the power of deep neural networks. A reoccurring challenge is how to enable a model to generate a rich variety of samples from the entire target distribution, rather…
This paper is to accompany the Census of Edge-Transitive Tetravalent Graphs, available at jan.ucc.nau.edu/~swilson/C4FullSite/index.html, which is a collection of all known edge-transitive graphs of valence 4 up to 512 vertices. The Census…
Generating text from structured inputs, such as meaning representations or RDF triples, has often involved the use of specialized graph-encoding neural networks. However, recent applications of pretrained transformers to linearizations of…
We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…
A 2-factor of a graph is a 2-regular spanning subgraph. For a graph $G$ and an independent set $I$ of $G$, let $\delta_G(I)$ denote the minimum degree of vertices contained in $I$. We show that (1) if every independent set $I$ of $G$…
High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove…
A $K_4$-decomposition of a graph is a partition of its edges into $K_4$s. A fractional $K_4$-decomposition is an assignment of a nonnegative weight to each $K_4$ in a graph such that the sum of the weights of the $K_4$s containing any given…
We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation: -- For any constant $k$, detecting $k$-paths and trees on $k$ nodes can be done in $O(1)$ rounds. --…
We introduce the standard decomposition, a way of decomposing a labeled graph into a sum of certain labeled subgraphs. We motivate this graph-theoretic concept by relating it to Connect Four decompositions of standard sets. We prove that…
The Four color problem is closely related to other branches of mathematics and practical applications. More than 20 of its reformulations are known, which connect this problem with problems of algebra, statistical mechanics and planning.…
Deep generative models (DGMs) have been widely developed for graph data. However, much less investigation has been carried out on understanding the latent space of such pretrained graph DGMs. These understandings possess the potential to…
Driven by successes in deep learning, computer vision research has begun to move beyond object detection and image classification to more sophisticated tasks like image captioning or visual question answering. Motivating such endeavors is…
We define a proportionally dense subgraph (PDS) as an induced subgraph of a graph with the property that each vertex in the PDS is adjacent to proportionally as many vertices in the subgraph as in the graph. We prove that the problem of…
We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number $k \ge 0$ of hamiltonian cycles, which is especially efficient for small $k$. Our main findings, combining applications of this algorithm…
Machine learning systems typically apply the same model to both easy and tough cases. This is in stark contrast with humans, who tend to evoke either fast (instinctive) or slow (analytical) thinking depending on the problem difficulty, a…