Related papers: Edge Constrained Eulerian Extensions
We provide a generating function for the (graded) dimensions of M. Kontsevich's graph complexes of ordinary graphs. This generating function can be used to compute the Euler characteristic in each loop order. Furthermore, we show that…
We consider optimization problems on manifolds with equality and inequality constraints. A large body of work treats constrained optimization in Euclidean spaces. In this work, we consider extensions of existing algorithms from the…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions…
We show that for every probability p with 0 < p < 1, computation of all-terminal graph reliability with edge failure probability p requires time exponential in Omega(m/ log^2 m) for simple graphs of m edges under the Exponential Time…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing…
A graph $G$ is called collapsible if for every even subset $R\subseteq V(G)$, there is a spanning connected subgraph $H$ of $G$ such that $R$ is the set of vertices of odd degree in $H$. A graph is the reduction of $G$ if it is obtained…
A metric probability space $M$ admits thresholds if the random geometric graph on $M$ has a threshold for every monotone graph property. We connect the existence of thresholds to the uniform expansion of $M$ and prove that all standard…
We define the Euler number of a bipartite graph on $n$ vertices to be the number of labelings of the vertices with $1,2,...,n$ such that the vertices alternate in being local maxima and local minima. We reformulate the problem of computing…
Disjoint paths problems are among the most prominent problems in combinatorial optimization. The edge- as well as vertex-disjoint paths problem, are NP-complete on directed and undirected graphs. But on undirected graphs, Robertson and…
We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum…
We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization…
In this paper extremal problems for uniform hypergraphs are studied in the general setting of hereditary properties. It turns out that extremal problems about edges are particular cases of a general analyic problem about a recently…
Compared to the classical binomial random (hyper)graph model, the study of random regular hypergraphs is made more challenging due to correlations between the occurrence of different edges. We develop an edge-switching technique for…
We introduce probability-graphons which are probability kernels that generalize graphons to the case of weighted graphs. Probability-graphons appear as the limit objects to study sequences of large weighted graphs whose distribution of…
For each natural number $n$ we determine, both asymptotically and exactly, the maximum number of edges an induced subgraph of order $n$ of the $d$-dimension a grid graph ${\ints}^d$ can have. The asymptotic bound is obtained by using a…
We consider entropy-optimal graphons associated with extreme and near-extreme constraints on the densities of edges and triangles. We prove that the optimizers for near-extreme constraints are unique and multipodal and are perturbations of…
Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes…
In the paper we give a lower bound for the number of vertices of a given graph using its chromatic number. We find the graphs for which this bound is exact. The results are applied in the theory of Foklman numbers.