Given a graph G and a subset W ⊆ V (G), a Steiner W -tree is a tree of minimum order that contains all of W . Let S(W ) denote the set of all vertices in G that lie on some Steiner W -tree; we call S(W ) the Steiner interval of W . If S(W ) = V (G), then we call W a Steiner set of G. The minimum order of a Steiner set of G is called the Steiner number of G. Given two vertices u, v in G, a short...

Mosquitoes are a great threat to human health date and subject of interdisciplinary research involving scientists from many areas. Recently much attention has been put novel approaches mosquito repellent products that involve the use materials, such as carbon nanomaterials, where it is essential determine their properties. This discusses full molecular characterization nanotubes (CNTs) produced...

Tony Low,1,2,3,*,† Michael Engel,1,4,† Mathias Steiner,4 and Phaedon Avouris1 1IBM T. J. Watson Research Center, 1101 Kitchawan Road, Yorktown Heights, New York 10598, USA 2Department of Physics and Electrical Engineering, Columbia University, New York, New York 10027, USA 3Department of Electrical & Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA 4IBM Research-...

Sensitivity and noise in GC–MS: Achieving low limits of detection for difficult analytes Alexander B. Fialkov a, Urs Steiner b, Steven J. Lehotay c, Aviv Amirav a,∗ a School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel b Varian Inc., 3645 Enochs Street, Santa Clara, CA 95051, USA c United States Department of Agriculture, Agricultural Research Ser...

We give a characterization of a current assignment on the bipartite Möbius ladder graph with 2n + 1 rungs. Such an assignment yields an index one current graph with current group Z12n+7 that generates an orientable face 2-colorable triangular embedding of the complete graph K12n+7 or, equivalently, an orientable biembedding of two cyclic Steiner triple systems of order 12n+7. We use our charact...

We consider the problem of constructing Steiner minimum trees for a metric defined by a polygonal unit circle (corresponding to σ ≥ 2 weighted legal orientations in the plane). A linear-time algorithm to enumerate all angle configurations for degree three Steiner points is given. We provide a simple proof that the angle configuration for a Steiner point extends to all Steiner points in a full S...

The Harary-Hill conjecture states that for every n > 0 the complete graph on n vertices Kn, the minimum number of crossings over all its possible drawings equals H(n) := 1 4 ⌊n 2 ⌋⌊n− 1 2 ⌋⌊n− 2 2 ⌋⌊n− 3 2 ⌋ . So far, the lower bound of the conjecture could only be verified for arbitrary drawings of Kn with n ≤ 12. In recent years, progress has been made in verifying the conjecture for certain ...

We consider a new Steiner tree problem, called vertex-cover-weighted Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a given vertex-weighted undirected graph. Since it is included by the Steiner tree activation problem, the problem admits an O(logn)-approximation algorithm in g...