We use basic results from graph theory to design two algorithms for constructing 3-dimensional, intersection-free orthogonal grid drawings of n vertex graphs of maximum degree 6. Our first algorithm gives drawings bounded by an O(x/~ ) • O(x/~ • O(v~ ) box; each edge route contains at most 7 bends. The best previous result generated edge routes containing up to 16 bends per route. Our second al...

Abstract We prove that if M and N are finitary matroids on a common countable edge set E then they admit independent I such there is bipartition = ? for which ? spans in N. It answers positively the Matroid Intersection Conjecture of Nash-Williams case.

An undirected graph G is called an EPT graph if it is the edge intersection graph of a family of paths in a tree. We call G a local EPT graph if it is the EPT graph of a collection of paths P which all share a common vertex. In this paper, we characterize the local EPT graphs which can be represented in a host tree with maximum degree h.

In this paper, low-complexity distributed fusion filtering algorithm for mixed continuous-discrete multisensory dynamic systems is proposed. To implement the algorithm a new recursive equations for local cross-covariances are derived. To achieve an effective fusion filtering the covariance intersection (CI) algorithm is used. The CI algorithm is useful due to its low-computational complexity fo...

We propose the following problem. A graph G is to be properly edge coloured such that any two adjacent vertices share at most k colours. We call this the k-intersection colouring. The minimum number of colours required for such a colouring is the kintersection chromatic index and is denoted χk. Let f be defined by fk(∆) = max G:∆(G)=∆ {χk(G)} We show that fk(∆) = Θ( 2 k ). We also discuss some ...

We compute the generating function for triangulations on a cylinder, with the restriction that all vertices belong to its boundary and that the intersection of a pair of different faces is either empty, a vertex or an edge. We generalize these results to maps with either constant ({k}-dissections) or unrestricted (unrestricted dissections) face degree. We apply singularity analysis to the resul...

The bend-number b(G) of a graph G is the minimum k such that G may be represented as the edge intersection graph of a set of grid paths with at most k bends. We confirm a conjecture of Biedl and Stern showing that the maximum bend-number of outerplanar graphs is 2. Moreover we improve the formerly known lower and upper bound for the maximum bend-number of planar graphs from 2 and 5 to 3 and 4, ...

Abstract. A BDDC (balancing domain decomposition by constraints) algorithm is developed for elliptic problems with mortar discretizations for geometrically non-conforming partitions in both two and three spatial dimensions. The coarse component of the preconditioner is defined in terms of one mortar constraint for each edge/face which is an intersection of the boundaries of a pair of subdomains...

Contact determination in terms of edge-face intersection tests permits handling nonconvex polyhedra directly, without decomposing them into convex entities, which saves the decomposition time and jects, modeled as convex polyhedra or polygon soups, and the goal is to determine when and where interference may occur. To this end, many techniques to encapsulate possiThe International Journal of Ro...

This document presents an overview to the clustComp package, which is a collection of tools developed for the comparison and the visualisation of relationships between two clusterings, either flat versus flat or flat versus hierarchical. Both situations are addressed by representing clusters as nodes in a weighted bipartite graph, where each layer corresponds to one of the clusterings under com...