We give a simple proof for a theorem of Katchalski, Last, and Valtr, asserting that the maximum number of edges in a geometric graph G on n vertices with no pair of parallel edges is at most 2n− 2. We also give a strengthening of this result in the case where G does not contain a cycle of length 4. In the latter case we show that G has at most 3 2 (n − 1) edges.

the aim of this work is to find an efficient aerodynamic-based design algorithm for projectile fins and configuration shape optimization. three-dimensional supersonic flow over a projectile with fins at much number 5 and one degree angle of attack was studied. the runge-kutta method and multi-block technique was used to solve the governing equations. a basic configuration was assumed for the fi...

All graphs considered here are finite simple graphs, i.e., graphs without loops, multiple edges or directed edges. For a graph G = (V, E), where V is a vertex set and E is an edge set, we write sometimes V (G) for V and E(G) for E to avoid ambiguity. We shall write G \ v instead of G V \{v} = (V \ {v}, E ∩ 2 V \{v}), the subgraph induced by V \ {v}. A vertex v ∈ V (G) is called a cut-vertex of ...

Kuratowski’s famous theorem of 1930 [6] asserts that a graph is planar if and only if it does not topologically contain K5 or K3,3. (Graphs are finite, and may have loops or multiple edges. A graph G topologically contains H if we may obtain a graph isomorphic to H from some subgraph of G by suppressing some divalent vertices.) There arose in the 1930’s the proposal to lind parallels to this th...

A topological drawing of a graph is fan-planar if for each edge e the edges crossing e have a common endpoint on the same side of e, and a fan-planar graph is a graph admitting such a drawing. Equivalently, this can be formulated by two forbidden patterns, one of which is the configuration where e is crossed by two independent edges and the other where e is crossed by incident edges with the co...

A novel architecture for the testing of enhanced data rates for GSM evolution (EDGE) networks is proposed, in which a reconfigurable radio platform is used to implement up to 16 EDGE physical layers in a RF baseband module (RFBBM). When the RFBBM is used in conjunction with a line server unit (LSU), a complete mobile station emulator (MSE) is formed. In this paper, the implementation and interf...

In cellular traffic offloading through opportunistic mobile networks, existing schemes rely on the assumption that data can be entirely transmitted at each contact. However, transmission probability exponentially decreases as data size increases. That is, the contact duration in each contact might be insufficient for delivering large data. The objective of this paper is to find an optimal traff...

We study and generalize the duplication model of Pastor-Satorras et al. [25]. This model generates a graph by iteratively “duplicating” a randomly chosen node as follows: We start at t0 with a fixed graph G(t0) of size t0. At each step t > t0 a new node vt is added. The node vt selects an existing node u from V (G(t − 1)) = {v1, ..., vt−1} uniformly at random (uar). The node vt then connects to...

We study gluino decays in the Minimal Supersymmetric Standard Model (MSSM) with squark generation mixing. We show that the effect of this mixing on the gluino decay branching ratios can be very large in a significant part of the MSSM parameter space despite the very strong experimental constraints on quark flavour violation (QFV) from B meson observables. Especially we find that under favourabl...