An Sq[t,k,v] q-Steiner system is a collection of k-dimensional subspaces of the v-dimensional vector space Fq over the finite field Fq with q elements, called blocks, such that each t-dimensional subspace of Fq is contained in exactly one block. The smallest admissible parameters for which a q-Steiner system could exist is S2[2,3,7]. Up to now the issue whether q-Steiner systems with these para...

We present a new visualization technique, called (Reconfigurable Disc Tree) which can alleviate the disadvantages of cone trees significantly for large hierarchies while maintaining its context of using 3D depth. In , each node is associated with a disc around which its children are placed. Using discs instead of cones as the basic shape in has several advantages: significant reduction of occlu...

Unicellular maps are a natural generalisation of plane trees to higher genus surfaces. In this article we study covered maps, which are maps together with a distinguished unicellular spanning submap. We prove that the covered maps of genus g with n edges are in bijection with pairs made of a plane tree with n edges and a bipartite unicellular map of genus g with n +1 edges. This generalises to ...

Status of this Memo This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited. Abstract This document specifies an ATM-based protocol for communication between ST2+ agents. The ST2+ over ATM protocol supports the matching of one hop in an ST2+ tree-structure stream with one ATM connection. In this docu...

Tree decompositions were developed by Robertson and Seymour [21]. Since then algorithms have been developed to solve intractable problems efficiently for graphs of bounded treewidth. In this paper we extend tree decompositions to allow cycles to exist in the decomposition graph; we call these new decompositions plane decompositions because we require that the decomposition graph be planar. Firs...

Asymptotic subcone of an unbounded metric space is another metric space, capturing the structure of the original space at infinity. In this paper we define a functional metric space S which is an asymptotic subcone of the hyperbolic plane. This space is a real tree branching at every its point. Moreover, it is a homogeneous metric space such that any real tree with countably many vertices can b...

A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimal possible total length. The Steiner ratio for a metric space is the largest lower bound for the ratio of lengths between a minimum Steiner tree and a minimum spanning tree on the same set of points in the metric space. Du et al. (1993) conjectured that the Steiner ratio on a normed plan...

Tree decompositions were developed by Robertson and Seymour [21]. Since then algorithms have been developed to solve intractable problems efficiently for graphs of bounded treewidth. In this paper we extend tree decompositions to allow cycles to exist in the decomposition graph; we call these new decompositions plane decompositions because we require that the decomposition graph be planar. Firs...

In this work we study edge weights for two specific families of increasing trees, which include binary increasing trees and plane oriented recursive trees as special instances, where plane-oriented recursive trees serve as a combinatorial model of scale-free random trees given by the m = 1 case of the BarabásiAlbert model. An edge e = (k, l), connecting the nodes labeled k and l, respectively, ...