An edge cover C of an undirected graph is a set of edges such that every vertex has an adjacent edge in C. We show that a Glauber dynamics Markov chain for edge covers mixes rapidly for graphs with degrees at most three. Glauber dynamics have been studied extensively in the statistical physics community, with special emphasis on lattice graphs. Our results apply, for example, to the hexagonal l...

A k-decomposition of a tree is a process in which the tree is recursively partitioned into k edge-disjoint subtrees until each subtree contains only one edge. We investigated the problem how many levels it is sufficient to decompose the edges of a tree. In this paper, we show that any n-edge tree can be 2-decomposed (and 3decomposed) within at most 1.44 log n (and log n respectively) levels. Ex...

In this note we report on our recent work, still in progress, regarding Folkman numbers. Let f(2, 3, 4) denote the smallest integer n such that there exists a K4– free graph of order n having that property that any 2–coloring of its edges yields at least one monochromatic triangle. It is well–known that such a number must exist [4,10]. For almost twenty years the best known upper bound, given b...

Let (P,≺) be a finite poset and let G be its comparability graph. If cl(G) is the clutter of maximal cliques of G, we prove that cl(G) satisfies the maxflow min-cut property and that its edge ideal is normally torsion free. We prove that edge ideals of complete admissible uniform clutters are normally torsion free. The normality of a monomial ideal is expressed in terms of blocking polyhedra an...

Wavelet-based image coders optimally represent smooth regions and isolated point singularities. However, w av elet coders are less adept at representing perceptually important edge singularities, and coding performance su ers signi cantly as a result. In this paper, w epropose a no veltw o-stageimage coder framework based on modeling images as edge cartoons + textures. In stage 1, w einfer and ...

The degree-constrained subgraphs decomposition problem, such as an f-coloring, an f-factorization, and a [ g, f ]-factorization, is to decompose a given graph G=(V, E) to edge-disjoint subgraphs degree-constrained by integer-valued functions f and g on V. In this paper we show that the problem can be simply reduced to the edge-coloring problem in polynomial-time. That is, for any positive integ...

We investigate the topology and combinatorics of a topological space called the edge-product space that is generated by the set of edge-weighted finite labelled trees. This space arises by multiplying the weights of edges on paths in trees, and is closely connected to tree-indexed Markov processes in molecular evolutionary biology. In particular, by considering combinatorial properties of the T...

We give a constant factor approximation algorithm for the Asymmetric Traveling Salesman Problem on shortest path metrics of directed graphs with two different edge weights. For the case of unit edge weights, the first constant factor approximation was given recently in [Sve15]. This was accomplished by introducing an easier problem called Local-Connectivity ATSP and showing that a good solution...

This article presents a technical demonstration of a system for determining the threedimensional spatial location of complexly shaped, thin-walled sheet metal parts grasped by robots during assembly. For successful part assembly, the precise location of grasped parts (essential for successful mating of parts) must be achieved. A localization system is implemented to determine the accurate posit...

In this paper, we discuss the vertex space domain decomposition method (VSDDM) for solving the algebraic system of equations which arise from the discretization of symmetric and positive de nite elliptic boundary value problems via nite element methods on general unstructured meshes. Our theory does not require that the subdomains are shape regular and coarse grid is nested to the ne grid. Furt...