Colouring (Pr + Ps)-Free Graphs

The k-Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a fixed integer k such that no two adjacent vertices are coloured alike. If each vertex u must be assigned a colour from a prescribed list L(u)⊆{1,…,k}, then we obtain the List k-Colouring problem. A graph G is H-free if G does not contain H as an induced subgraph. We continue an extensive study into the complexity of these two problems for H-free graphs. The graph Pr+Ps is the disjoint union of the r-vertex path Pr and the s-vertex path Ps. We prove that List 3-Colouring is polynomial-time solvable for (P2+P5)-free graphs and for (P3+P4)-free graphs. Combining our results with known results yields complete complexity classifications of 3-Colouring and List 3-Colouring on H-free graphs for all graphs H up to seven vertices

Lambda production in 40 A GeV/c Pb-Au collisions

During the 1999 lead run, CERES has measured hadron and electron-pair production at 40 A GeV/c beam momentum with the spectrometer upgraded by the addition of a radial TPC. Here the analysis of lambda and antilambda will be presented.Comment: 8 pages, 8 figures. 6th International Conference on Strange Quarks in Matter, Frankfurt 200

Flow and non-flow event anisotropies at the SPS

A study of differential elliptic event anisotropies (v_2) of charged particles and high-pt pions in 158 AGeV/c Pb+Au collisions is presented. Results from correlations with respect to the event plane and from two-particle azimuthal correlations are compared. The latter give systematically higher v_2 values at pt>1.2GeV/c providing possibly an evidence of a non-flow semihard component.Comment: 4 pages, 6 figures, Quark Matter 2002, Nantes, to appear in Nucl. Phys.

Universal Pion Freeze-out in Heavy-Ion Collisions

Based on an evaluation of data on pion interferometry and on particle yields at mid-rapidity, we propose a universal condition for thermal freeze-out of pions in heavy-ion collisions. We show that freeze-out occurs when the mean free path of pions lambda_f reaches a value of about 1 fm, which is much smaller than the spatial extent of the system at freeze-out. This critical mean free path is independent of the centrality of the collision and beam energy from AGS to RHIC.Comment: 5 pages, 3 figures, revised version resubmitted to PR

Colouring (Pr+Ps)-free graphs.

The k-Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a fixed integer k such that no two adjacent vertices are coloured alike. If each vertex u must be assigned a colour from a prescribed list L(u) subseteq {1,...,k}, then we obtain the List k-Colouring problem. A graph G is H-free if G does not contain H as an induced subgraph. We continue an extensive study into the complexity of these two problems for H-free graphs. We prove that List 3-Colouring is polynomial-time solvable for (P_2+P_5)-free graphs and for (P_3+P_4)-free graphs. Combining our results with known results yields complete complexity classifications of 3-Colouring and List 3-Colouring on H-free graphs for all graphs H up to seven vertices. We also prove that 5-Colouring is NP-complete for (P_3+P_5)-free graphs

Parton coalescence at RHIC

Using a covariant coalescence model, we study hadron production in relativistic heavy ion collisions from both soft partons in the quark-gluon plasma and hard partons in minijets. Including transverse flow of soft partons and independent fragmentation of minijet partons, the model is able to describe available experimental data on pion, kaon, and antiproton spectra. The resulting antiproton to pion ratio is seen to increase at low transverse momenta and reaches a value of about one at intermediate transverse momenta, as observed in experimental data at RHIC. A similar dependence of the antikaon to pion ratio on transverse momentum is obtained, but it reaches a smaller value at intermediate transverse momenta. At high transverse momenta, the model predicts that both the antiproton to pion and the antikaon to pion ratio decrease and approach those given by the perturbative QCD. Both collective flow effect and coalescence of minijet partons with partons in the quark-gluon plasma affect significantly the spectra of hadrons with intermediate transverse momenta. Elliptic flows of protons, Lambdas, and Omegas have also been evaluated from partons with elliptic flows extracted from fitting measured pion and kaon elliptic flows, and they are found to be consistent with available experimental data.Comment: 12 pages, 11 figure

The structure of 99^{99}Ru from (α\alpha,3n) reaction

The results of in-beam investigations of excited states of $^{99}$Ru using the $^{98}$Mo($\alpha$, 3n) reaction are presented. Angular distributions of $\gamma$–rays and $\gamma$–$\gamma$ coincidences have been measured. Excited states have been identified up to an energy of E = 5603 keV and spin of I$^{\pi}$ = 31/2$^{-}$. Mean lifetimes $\tau$ have been determined using the DSA method for eleven levels. Aligned angular momenta are discussed and the probable $(\nu h_{11/2})$ origin of a backbending at frequency about 0.5 MeV was confirmed. The possible role of $(\nu d_{5/2})$ alignment at frequencies above 0.5 MeV was pointed out

Colouring (Pr+Ps)-free graphs

The k-Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a fixed integer k such that no two adjacent vertices are coloured alike. If each vertex u must be assigned a colour from a prescribed list L(u) subseteq {1,...,k}, then we obtain the List k-Colouring problem. A graph G is H-free if G does not contain H as an induced subgraph. We continue an extensive study into the complexity of these two problems for H-free graphs. We prove that List 3-Colouring is polynomial-time solvable for (P_2+P_5)-free graphs and for (P_3+P_4)-free graphs. Combining our results with known results yields complete complexity classifications of 3-Colouring and List 3-Colouring on H-free graphs for all graphs H up to seven vertices. We also prove that 5-Colouring is NP-complete for (P_3+P_5)-free graphs

New results from CERES

We will focus here on results from the 1999 data taking period, where 8 M Pb+Au events at 40 AGeV were recorded. Since the new readout system of the TPC was not yet properly working, this data set is limited in terms of statistics, and momentum resolution. Nevertheless, this data sample at lower beam energy allows to study initial conditions different from the ones at top SPS energy. This can be very useful to disentangle temperature and baryon density driven modifications of the dilepton spectrum. (15 refs)