Related papers: Generalizations of interval and proper interval gr…
The Constraint Satisfaction Problem (CSP) has been intensively studied in many areas of computer science and mathematics. The approach to the CSP based on tools from universal algebra turned out to be the most successful one to study the…
The cut sets of a graph are special sets of vertices whose removal disconnects the graph. They are fundamental in the study of binomial edge ideals, since they encode their minimal primary decomposition. We introduce the class of accessible…
In this paper we deal with a subclass of chordal graphs, which are simultaneously strictly chordal and interval, the strictly interval graphs. We present a new characterization of the class that leads to a simple linear recognition…
We give a complete characterization of mixed unit interval graphs, the intersection graphs of closed, open, and half-open unit intervals of the real line. This is a proper superclass of the well known unit interval graphs. Our result solves…
We recall several categories of graphs which are useful for describing homotopy-coherent versions of generalized operads (e.g. cyclic operads, modular operads, properads, and so on), and give new, uniform definitions for their morphisms.…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
We provide necessary and sufficient conditions for simplicial complexes whose determinantal facet ideals admit reduced Grobner bases under diagonal term orders. Building on and extending foundational results for binomial edge ideals and…
Let d = (d1, d2, ..., dn) be a vector of non-negative integers with even sum. We prove some basic facts about the structure of a random graph with degree sequence d, including the probability of a given subgraph or induced subgraph.…
We generalize the fundamental graph-theoretic notion of chordality for higher dimensional simplicial complexes by putting it into a proper context within homology theory. We generalize some of the classical results of graph chordality to…
Separated graphs provide a powerful combinatorial tool for approximating dynamical systems. This paper details the explicit construction of Bratteli-like separated graphs -- a generalization of classical Bratteli diagrams -- that encode the…
Independent sets play a key role into the study of graphs and important problems arising in graph theory reduce to them. We define the monomial ideal of independent sets associated to a finite simple graph and describe its homological and…
In this paper we extend one direction of Fr\"oberg's theorem on a combinatorial classification of quadratic monomial ideals with linear resolutions. We do this by generalizing the notion of a chordal graph to higher dimensions with the…
The paper surveys recent progress in understanding geometric, topological and combinatorial properties of large simplicial complexes, focusing mainly on ampleness, connectivity and universality. In the first part of the paper we concentrate…
We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.
In this article we are introducing combinatorial spectra of graphs, this is a generalization of $H$-Hamiltonian spectra. The main motivation was to made from $H$-Hamiltonian spectra an operation and develop some algebra in this field. An…
The notion of a generalized scale emerged in recent joint work with Afsar-Brownlowe-Larsen on equilibrium states on C*-algebras of right LCM monoids, where it features as the key datum for the dynamics under investigation. This work…
We develop a theory of average sizes of kernels of generic matrices with support constraints defined in terms of graphs and hypergraphs. We apply this theory to study unipotent groups associated with graphs. In particular, we establish…
We collect some general results on graph limits associated to hereditary classes of graphs. As examples, we consider some classes defined by forbidden subgraphs and some classes of intersection graphs, including triangle-free graphs,…
This work introduces a general theory of universal pseudomorphisms and develops their connection to diagrammatic coherence. The main results give hypotheses under which pseudomorphism coherence is equivalent to the coherence theory of…
Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs. In this paper we introduce the concept of proper thinness, such that graphs with bounded proper thinness generalize proper interval graphs. We study…