Related papers: Mixtures of Discrete Decomposable Graphical Models
Let $G$ be a finite connected simple graph with $d$ vertices and let $\Pc_G \subset \RR^d$ be the edge polytope of $G$. We call $\Pc_G$ \emph{decomposable} if $\Pc_G$ decomposes into integral polytopes $\Pc_{G^+}$ and $\Pc_{G^-}$ via a…
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…
In this paper we examine some natural ideal conditions and show how graphs can be defined that give a visualization of these conditions. We examine the interplay between the multiplicative ideal theory and the graph theoretic structure of…
For a graph $G=(V,E),$ a matching $M$ is a set of independent edges. The topic of matchings is well studied in graph theory. In this paper many varieties of matchings are discussed.
Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For finite graphs one popular way to compute upper bounds for…
We present a complete computational classification of the combinatorial types of hyperplane sections, or slices, of the regular cube up to dimension six. For each dimension, we determine the exact number of distinct combinatorial types.…
Coloured graphical models are Gaussian statistical models determined by an undirected coloured graph. These models can be described by linear spaces of symmetric matrices. We outline a relationship between the symmetries of the graph and…
Let $G$ be a simple graph with binomial edge ideal $J_G$. We prove how to calculate the multidegree of $J_G$ based on combinatorial properties of $G$. In particular, we study the set $S_{\min}(G)$ defined as the collection of subsets of…
We find a class of block graphs whose binomial edge ideals have minimal regularity. As a consequence, we characterize the trees whose binomial edge ideals have minimal regularity. Also, we show that the binomial edge ideal of a block graph…
We focus our attention on well-covered graphs that are vertex decomposable. We show that for many known families of these vertex decomposable graphs, the set of shedding vertices forms a dominating set. We then construct three new infinite…
The usual univariate interpolation problem of finding a monic polynomial f of degree n that interpolates n given values is well understood. This paper studies a variant where f is required to be composite, say, a composition of two…
The paper presents a subclass of the class of MD5-algebras and MD5-groups, i.e., five dimensional solvable Lie algebras and Lie groups such that their orbits in the co-adjoint representation (K-orbit) are orbit of zero or maximal dimension.…
A $k$-star decomposition of a graph is a partition of its edges into $k$-stars (i.e., $k$ edges with a common vertex). The paper studies the following problem: for what values of $k>d/2$ does the random $d$-regular graph have a $k$-star…
We consider the multiplier ideals of the ideal of a reduced union of lines through the origin in C^3. For general arrangements of lines, we calculate the multiplier ideals.
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
We study the set of all decompositions (clusterings) of a graph through its characterization as a set of lifted multicuts. This leads us to practically relevant insights related to the definition of a class of decompositions by must-join…
Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine…
We introduce the concept of multiplication matrices for ideals of projective dimension zero. We discuss various applications and in particular, we give a new algorithm to compute the variety of an ideal of projective dimension zero.
We investigate the class of models of a general dependent theory. We continue math.LO/0702292 in particular investigating so called "decomposition of types"; thesis is that what holds for stable theory and for Th(Q,<) hold for dependent…
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…