We prove that for every k > 0 there is an integer n0(k) such that, for every n > n0, there exists a hypohamiltonian graph which has order n and crossing number k.

We prove that the crossing number of a graph decays in a " continuous fashion " in the following sense. For any ε > 0 there is a δ > 0 such that for a sufficiently large n, every graph G with n vertices and m ≥ n 1+ε edges, has a subgraph G ′ of at most (1 − δ)m edges and crossing number at least (1 − ε)cr(G). This generalizes the result of J. Fox and Cs. Tóth.

Résumé We prove that two disjoint graphs must always be drawn separately on the Klein bottle in order to minimize the crossing number of the whole drawing.

PAGE INTRODUCTION .................................................................. I35 Coincidence of widely separated regions. , 138 Coincidence in the second chromosome. 146 Coincidence in the third chromosome. 148 Coincidence in other forms 148 The mechanism of crossing over 148 Triple crossing over .: .. I49 Maximum and minimum coincidence. I53 The distance between the breaking points in ...

The crossing number cr(G) of a graph G is the minimum possible number of edge-crossings in a drawing of G, the pair-crossing number pcr(G) is the minimum possible number of crossing pairs of edges in a drawing of G, and the odd-crossing number ocr(G) is the minimum number of pairs of edges that cross an odd number of times. Clearly, ocr(G) ≤ pcr(G) ≤ cr(G). We construct graphs with 0.855 · pcr(...

For any simple graph G = (V, E), we can define four types of crossing number: crossing number, rectilinear crossing number, odd-crossing number, and pairwise crossing number. We discuss the relationship of them.

Chronic total occlusions (CTOs) represent the "last frontier" of percutaneous interventions. The main technical challenges lies in crossing the guidewire into the distal true lumen, which is primarily due to three problems: device buckling during initial puncture, inadequate visualization, and the inability to actively navigate through the CTO. To improve the success rate and to identify future...

Speech can be modeled as short bursts of vocal energy separated by silence gaps. During typical conversation, talkspurts comprise only 40% of each party’s speech and remaining 60% is silence. Communication systems can achieve spectral gain by disconnecting the users from the spectral resource during silence periods. This letter develops a simple and efficient Voice Activity Detection (VAD) algo...

In this paper, we proposed a system for automatic classification of speech. A speech signal contains three different regions voiced, unvoiced and silence. In the proposed system, Zero-Crossing rate and short term energy are used in a fuzzy logic control this classification. Arabic digits of the KSU database is used to test our proposed method. The proposed method achieves 2.5 % error between hu...

In this paper, we present a novel principal component analysis (PCA) based approach towards modeling the object trajectory in a video clip. An eigenspace decomposition of highdimensional trajectory data leads to very compact representation, which is then used as indexing structure. To cutback on PCA computation during indexing, we first segment the trajectories into atomic subtrajectories using...