Disjoint edges in topological graphs and the tangled-thrackle conjecture

It is shown that for a constant $t\in \mathbb{N}$, every simple topological graph on $n$ vertices has $O(n)$ edges if it has no two sets of $t$ edges such that every edge in one set is disjoint from all edges of the other set (i.e., the complement of the intersection graph of the edges is $K_{t,t}$-free). As an application, we settle the \emph{tangled-thrackle} conjecture formulated by Pach, Radoi\v{c}i\'c, and T\'oth: Every $n$-vertex graph drawn in the plane such that every pair of edges have precisely one point in common, where this point is either a common endpoint, a crossing, or a point of tangency, has at most $O(n)$ edges

Thrackles: An improved upper bound

A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, except that every pair of edges that do not share a vertex are allowed to cross an odd number of times. It is also shown that the maximum number of edges of a quasi-thrackle on n vertices is 3/2(n-1), and that this bound is best possible for infinitely many values of n. © Springer International Publishing AG 2018

Measurements of the transverse-momentum-dependent cross sections of J /ψ production at mid-rapidity in proton+proton collisions at s =510 and 500 GeV with the STAR detector

We present measurements of the differential cross sections of inclusive J/ψ meson production as a function of transverse momentum (pTJ/ψ) using the μ+μ- and e+e- decay channels in proton+proton collisions at center-of-mass energies of 510 and 500 GeV, respectively, recorded by the STAR detector at the Relativistic Heavy Ion Collider. The measurement from the μ+μ- channel is for

Measurement of inclusive J/ψ suppression in Au+Au collisions at sNN=200 GeV through the dimuon channel at STAR

J/ψ suppression has long been considered a sensitive signature of the formation of the Quark-Gluon Plasma (QGP) in relativistic heavy-ion collisions. In this letter, we present the first measurement of inclusive J/ψ production at mid-rapidity through the dimuon decay channel in Au+Au collisions at sNN=200 GeV with the STAR experiment. These measurements became possible after the installation of the Muon Telescope Detector was completed in 2014. The J/ψ yields are measured in a wide transverse momentum (pT) range of 0.15 GeV/c to 12 GeV/c from central to peripheral collisions. They extend the kinematic reach of previous measurements at RHIC with improved precision. In the 0-10% most central collisions, the J/ψ yield is suppressed by a factor of approximately 3 for pT>5 GeV/c relative to that in p+p collisions scaled by the number of binary nucleon-nucleon collisions. The J/ψ nuclear modification factor displays little dependence on pT in all centrality bins. Model calculations can qualitatively describe the data, providing further evidence for the color-screening effect experienced by J/ψ mesons in the QGP

Charge-dependent pair correlations relative to a third particle in p + Au and d + Au collisions at RHIC

Quark interactions with topological gluon configurations can induce chirality imbalance and local parity violation in quantum chromodynamics. This can lead to electric charge separation along the strong magnetic field in relativistic heavy-ion collisions – the chiral magnetic effect (CME). We report measurements by the STAR collaboration of a CME-sensitive observable in p+Au and d+Au collisions at 200 GeV, where the CME is not expected, using charge-dependent pair correlations relative to a third particle. We observe strong charge-dependent correlations similar to those measured in heavy-ion collisions. This bears important implications for the interpretation of the heavy-ion data

Bulk properties of the system formed in Au+Au collisions at sNN =14.5 GeV at the BNL STAR detector

We report systematic measurements of bulk properties of the system created in Au+Au collisions at sNN=14.5 GeV recorded by the STAR detector at the Relativistic Heavy Ion Collider (RHIC). The transverse momentum spectra of π±, K±, and p(p) are studied at midrapidity (|y|<0.1) for nine centrality intervals. The centrality, transverse momentum (pT), and pseudorapidity (η) dependence of inclusive charged particle elliptic flow (v2), and rapidity-odd charged particles directed flow (v1) results near midrapidity are also presented. These measurements are compared with the published results from Au+Au collisions at other energies, and from Pb+Pb collisions at sNN=2.76 TeV. The results at sNN=14.5 GeV show similar behavior as established at other energies and fit well in the energy dependence trend. These results are important as the 14.5-GeV energy fills the gap in μB, which is of the order of 100 MeV, between sNN=11.5 and 19.6 GeV. Comparisons of the data with UrQMD and AMPT models show poor agreement in general