A group G is of type Fn if there is a K(G, 1) complex that has finite n-skeleton. It is of type F∞, if it is of type Fn for all n ∈ N. Here the property F1 is equivalent to G being finitely generated and the property F2 equivalent to being finitely presented. An interesting question in the study of these finiteness properties is how they change, if the group under consideration is changed. One ...

Using graph based approaches save trajectories for manipulators can be planned fast. It is favorable to use techniques that allow to plan at least some motions from the beginning of the graph construction process, and that can be improved incrementally. We introduce an approach that fulllls the above requirements using random conngurations for graph construction (unless speciic tasks are given)...

COLLECTING, understanding, and interpreting data are key skills that all students should master (8, 12, 22, 33). Research on graph interpretation and basic construction is extensive, and student difficulties, primarily in K-12 type settings, have been well documented [e.g., graph choice (30, 32, 45), labels for axes (30, 32), variables (45), and scaling axes (1, 7, 32, 34)]. Although many instr...

The paper contains a construction of a universal countable graph, different from the Rado graph, such that for any of its vertices both the neighbourhood and the non-neighbourhood induce subgraphs isomorphic to the whole graph. This solves an open problem proposed by A. Bonato; see Problem 20 in [5]. We supply a construction of several non-isomorphic graphs with the property, and consider tourn...

A construction tree is a set of shape generation processes commonly produced with CAD modelers during a design process of B-Rep objects. However, a construction tree does not bring all the desired properties in many configurations: dimension modifications, idealization processes,. . . Generating a non trivial set of generative processes, possibly forming a construction graph, can significantly ...

Computer vision and pattern recognition techniques based on graph theory constitute a wellestablished research area due mainly to their success in efficiently representing and solving many related problems such as image segmentation [1], [2] and saliency estimation [9]. Graph construction for the related problems is traditionally performed manually. This construction involves three major steps:...

In this paper, we consider how self-description can be realized for construction and execution in a single framework of a variant of graph rewriting systems, called graph rewriting automata. As an example of self-description for construction, a self-replication based on a self-description is shown. Meta-node structure is introduced for selfdescription for execution that enables us to embed rule...

It is the powering construction which will be of interest to us. Essentially, the powering construction works by taking a constraint graph, and building a t-fold power graph, which collects all paths of length t emanating from a node. The proof (i.e. the labelling of the constraint graph) now must supply versions of labels of nodes collected at each composite node – of course, the constraints b...

We investigate how a straight skeleton can be used to approximate a motorcycle graph. We explain how to construct a planar straight-line graph G such that the straight skeleton of G reveals the motorcycle graph of M , for every given finite set M of motorcycles. An application of our construction is a proof of the Pcompleteness of the construction problem of straight skeletons of planar straigh...