Related papers: Series-parallel graphs and hypercube degeneracy
We develop the first parallel graph coloring heuristics with strong theoretical guarantees on work and depth and coloring quality. The key idea is to design a relaxation of the vertex degeneracy order, a well-known graph theory concept, and…
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…
Graph representations of solid state materials that encode only interatomic distance lack geometrical resolution, resulting in degenerate representations that may map distinct structures to equivalent graphs. Here we propose a hypergraph…
We study the classic problem of subgraph counting, where we wish to determine the number of occurrences of a fixed pattern graph $H$ in an input graph $G$ of $n$ vertices. Our focus is on bounded degeneracy inputs, a rich family of graph…
The paper deals with partitions of hypergraphs into induced subhypergraphs satisfying constraints on their degeneracy. Our hypergraphs may have multiple edges, but no loops. Given a hypergraph $H$ and a sequence $f=(f_1,f_2, \ldots, f_p)$…
A subgraph of the $n$-dimensional hypercube is called 'layered' if it is a subgraph of a layer of some hypercube. In this paper we show that there exist subgraphs of the cube of arbitrarily large girth that are not layered. This answers a…
There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…
We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued…
We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of designs.
Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…
Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…
In this work, we introduce a novel evaluation framework for generative models of graphs, emphasizing the importance of model-generated graph overlap (Chanpuriya et al., 2021) to ensure both accuracy and edge-diversity. We delineate a…
We introduce the notion of q-analogs of strongly regular graphs and give several examples of such structures. We prove a necessary condition on the parameters, show the connection to designs over finite fields, and present a classification.
A hypergraph is called uniform when every hyperedge contains the same number of vertices, otherwise, it is called non-uniform. In the real world, many systems give rise to non-uniform hypergraphs, such as email networks and co-authorship…
From social networks to protein complexes to disease genomes to visual data, hypergraphs are everywhere. However, the scope of research studying deep learning on hypergraphs is still quite sparse and nascent, as there has not yet existed an…
The vertices of an interval graph represent intervals over a real line where overlapping intervals denote that their corresponding vertices are adjacent. This implies that the vertices are measurable by a metric and there exists a linear…
Conventionally used exponential random graphs cannot directly model weighted networks as the underlying probability space consists of simple graphs only. Since many substantively important networks are weighted, this limitation is…
We propose a new deep network structure for unconstrained face recognition. The proposed network integrates several key components together in order to characterize complex data distributions, such as in unconstrained face images. Inspired…
In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…
We propose a general multi-class visual recognition model, termed the Classifier Graph, which aims to generalize and integrate ideas from many of today's successful hierarchical recognition approaches. Our graph-based model has the…