Graph Treewidth and Geometric Thickness Parameters

Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for graphs of treewidth $k$, the maximum thickness and the maximum geometric thickness both equal $\lceil{k/2}\rceil$. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth $k$, the maximum book thickness equals $k$ if $k \leq 2$ and equals $k+1$ if $k \geq 3$. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215-221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity.Comment: A preliminary version of this paper appeared in the "Proceedings of the 13th International Symposium on Graph Drawing" (GD '05), Lecture Notes in Computer Science 3843:129-140, Springer, 2006. The full version was published in Discrete & Computational Geometry 37(4):641-670, 2007. That version contained a false conjecture, which is corrected on page 26 of this versio

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Technology in blood transfusion Clinical Haemotology. Vol. 3 No. 2. Blood Transfusion: The Impact of New Technologies. Ed. by Marcela Contreras. pp. x + 482. illustrated. R22,SO. Kent: Harcourt Brace Jovanovich. 1990.Oncology International Classification of Diseases for Oncology. 2nd ed. Ed. By C. Percy, V. van Holten and C. Muir. pp. xiv + 144. Geneva: WHO. 1990.Chronic fatigue syndrome Chronic Fatigue Syndrome: The Stnlggle for Health. Ed. by Jay A. Goldstein. pp. xiv + 177. illustrated. Beverley Hills: Chronic Fatigue Syndrome Institute. 1990. Respiratory medicineRespiratory Medicine. Ed. by R. A. L. Brewis, G. J. Gibson and D. M. Geddes. pp. xxi + 1559. illustrated. R85. London: Bailliere, Tindall. 1990.Cardiac hypertrophy and failure Research in Cardiac Hypertrophy and Failure. Ed. by B. Swynghedauw. pp. xvi + 696. illustrated. £65. London: John Libbey. 1990.Reconstructive surgery in gynaecology Reconstructive Surgery in Gynaecology. Red. deur P. G. Knapstein, V. Friedberg and B-U. Sevin. pp. xii + 281. illustrated. DM 298. Smttgart: Georg Thieme Verlag. 1990.Menslike anatomie Basiese Menslike Anatomie. Red. deur Linda de Jager. pp. 204, illustrated. Wetton: Juta. 1990. GIFT: from basics to clinics GIFr: From Basics to Clinics. Red. deur G. L. Capitanio, R. H. Asch, L. de Cecco and S. Croce. New York: Serono Symposia Publications from Raven Press.Environmental health Environmental Health Criteria. No. 88: Polychlorinated Dibenzopara-dioxins and Dibenzofurans. pp. 409. illustrated. Geneva: WHO. 1989.Genetic engineering Reshaping Life: Key Issues in Genetic Engineering. 2nd ed. Ed. by G. J. V. Nossal and Ross L. Coppel. pp. xii + 179. Australia: Cambridge University Press. 1989.Doctor-patient communication Talking With Patients: A Basic Clinical skin. Ed. by Philip R. Myerscough. pp. I + 148. illustrated. Oxford: Oxford University Press. 1989.

Cosmological Creation of D-branes and anti-D-branes

We argue that the early universe may be described by an initial state of space-filling branes and anti-branes. At high temperature this system is stable. At low temperature tachyons appear and lead to a phase transition, dynamics, and the creation of D-branes. These branes are cosmologically produced in a generic fashion by the Kibble mechanism. From an entropic point of view, the formation of lower dimensional branes is preferred and $D3$ brane-worlds are exponentially more likely to form than higher dimensional branes. Virtually any brane configuration can be created from such phase transitions by adjusting the tachyon profile. A lower bound on the number defects produced is: one D-brane per Hubble volume.Comment: 30 pages, 5 eps figures; v2 more references added; v3 section 4 slightly improve

Finding a moral homeground: appropriately critical religious education and transmission of spiritual values

Values-inspired issues remain an important part of the British school curriculum. Avoiding moral relativism while fostering enthusiasm for spiritual values and applying them to non-curricular learning such as school ethos or children's home lives are challenges where spiritual, moral, social and cultural (SMSC) development might benefit from leadership by critical religious education (RE). Whether the school's model of spirituality is that of an individual spiritual tradition (schools of a particular religious character) or universal pluralistic religiosity (schools of plural religious character), the pedagogy of RE thought capable of leading SMSC development would be the dialogical approach with examples of successful implementation described by Gates, Ipgrave and Skeie. Marton's phenomenography, is thought to provide a valuable framework to allow the teacher to be appropriately critical in the transmission of spiritual values in schools of a particular religious character as evidenced by Hella's work in Lutheran schools

Analysis of LIGO data for gravitational waves from binary neutron stars

We report on a search for gravitational waves from coalescing compact binary systems in the Milky Way and the Magellanic Clouds. The analysis uses data taken by two of the three LIGO interferometers during the first LIGO science run and illustrates a method of setting upper limits on inspiral event rates using interferometer data. The analysis pipeline is described with particular attention to data selection and coincidence between the two interferometers. We establish an observational upper limit of $\mathcal{R}<$1.7 \times 10^{2}$per year per Milky Way Equivalent Galaxy (MWEG), with 90coalescence rate of binary systems in which each component has a mass in the range 1--3$M_\odot$.Comment: 17 pages, 9 figure

Search for supersymmetry with a dominant R-parity violating LQDbar couplings in e+e- collisions at centre-of-mass energies of 130GeV to 172 GeV

A search for pair-production of supersymmetric particles under the assumption that R-parity is violated via a dominant LQDbar coupling has been performed using the data collected by ALEPH at centre-of-mass energies of 130-172 GeV. The observed candidate events in the data are in agreement with the Standard Model expectation. This result is translated into lower limits on the masses of charginos, neutralinos, sleptons, sneutrinos and squarks. For instance, for m_0=500 GeV/c^2 and tan(beta)=sqrt(2) charginos with masses smaller than 81 GeV/c^2 and neutralinos with masses smaller than 29 GeV/c^2 are excluded at the 95% confidence level for any generation structure of the LQDbar coupling.Comment: 32 pages, 30 figure

Intercalibration of the barrel electromagnetic calorimeter of the CMS experiment at start-up

Calibration of the relative response of the individual channels of the barrel electromagnetic calorimeter of the CMS detector was accomplished, before installation, with cosmic ray muons and test beams. One fourth of the calorimeter was exposed to a beam of high energy electrons and the relative calibration of the channels, the intercalibration, was found to be reproducible to a precision of about 0.3%. Additionally, data were collected with cosmic rays for the entire ECAL barrel during the commissioning phase. By comparing the intercalibration constants obtained with the electron beam data with those from the cosmic ray data, it is demonstrated that the latter provide an intercalibration precision of 1.5% over most of the barrel ECAL. The best intercalibration precision is expected to come from the analysis of events collected in situ during the LHC operation. Using data collected with both electrons and pion beams, several aspects of the intercalibration procedures based on electrons or neutral pions were investigated

Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events

The $B^0$-$\bar B^0$ oscillation frequency has been measured with a sample of 23 million \B\bar B pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives $\Delta m_d = 0.493 \pm 0.012{(stat)}\pm 0.009{(syst)}$ ps$^{-1}$.Comment: 7 pages, 1 figure, submitted to Physical Review Letter