Related papers: Bayesian/Graphoid intersection property for factor…
We present an alternate proof of a result of F\'eray and Reiner characterizing posets whose $P$-partition rings are complete intersections. This shortened proof relates the complete intersection property to a simple structural property of a…
Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable ``interlace polynomial'' for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and…
In this survey, we have attempted to show some developmental milestones on the characterizations of intersection graphs of hypergraphs. The theory of intersection graphs of hypergraphs has been a classical topic in the theory of special…
The set of factorizations of permutations in to $m$ transpositions of some symmetric group $\mathcal{S}_n$ is naturally in bijection with the set of graphs of order $n$ and size $m$ with both edges and vertices labeled. We define a notion…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
We discuss the property of (almost) complete intersection of LSS-ideals of graphs of some special forms, like trees, unicyclic, and bicyclic graphs. Further, we give a sufficient condition for the complete intersection property of twisted…
A graph property (i.e., a set of graphs) is induced-hereditary or additive if it is closed under taking induced-subgraphs or disjoint unions. If $\cP$ and $\cQ$ are properties, the product $\cP \circ \cQ$ consists of all graphs $G$ for…
Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying…
We consider three notions of connectivity and their interactions in partially ordered sets coming from reduced factorizations of an element in a generated group. While one form of connectivity essentially reflects the connectivity of the…
This work forms a foundational study of factorization homology, or topological chiral homology, at the generality of stratified spaces with tangential structures. Examples of such factorization homology theories include intersection…
The Feller property concerns the preservation of the space of functions vanishing at infinity by the semigroup generated by an operator. We study this property in the case of the Laplacian on infinite graphs with arbitrary edge weights and…
Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way…
Random graphs with latent geometric structure are popular models of social and biological networks, with applications ranging from network user profiling to circuit design. These graphs are also of purely theoretical interest within…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
We derive two finiteness properties as consequences of the geometrical non-degeneracy of an algebraic subvariety $W$ of a power of the multiplicative group, concerning the intersections of $W$ with translates of a subtorus $H$ of dimension…
In this paper a generalisation of the notion of polarity is exhibited which allows to completely describe, in an incidence-geometric way, the linear complexes of $h$-subspaces. A generalised polarity is defined to be a partial map which…
By extending the definition of boxicity, we extend a Helly-type result given by Danzer and Grumbaum on 2-piercings of family of boxes in $d$-dimensional Euclidian space by lowering the dimension of the boxes in the ambient space.
We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
We prove ``half-space" intersection properties in three settings: the hemisphere, half-geodesic balls in space forms, and certain subsets of Gaussian space. For instance, any two embedded minimal hypersurfaces in the sphere must intersect…