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

Universal Geometric Graphs

We introduce and study the problem of constructing geometric graphs that have few vertices and edges and that are universal for planar graphs or for some sub-class of planar graphs; a geometric graph is \emph{universal} for a class $\mathcal H$ of planar graphs if it contains an embedding, i.e., a crossing-free drawing, of every graph in $\mathcal H$. Our main result is that there exists a geometric graph with $n$ vertices and $O(n \log n)$ edges that is universal for $n$-vertex forests; this extends to the geometric setting a well-known graph-theoretic result by Chung and Graham, which states that there exists an $n$-vertex graph with $O(n \log n)$ edges that contains every $n$-vertex forest as a subgraph. Our $O(n \log n)$ bound on the number of edges cannot be improved, even if more than $n$ vertices are allowed. We also prove that, for every positive integer $h$, every $n$-vertex convex geometric graph that is universal for $n$-vertex outerplanar graphs has a near-quadratic number of edges, namely $\Omega_h(n^{2-1/h})$; this almost matches the trivial $O(n^2)$ upper bound given by the $n$-vertex complete convex geometric graph. Finally, we prove that there exists an $n$-vertex convex geometric graph with $n$ vertices and $O(n \log n)$ edges that is universal for $n$-vertex caterpillars.Comment: 20 pages, 8 figures; a 12-page extended abstracts of this paper will appear in the Proceedings of the 46th Workshop on Graph-Theoretic Concepts in Computer Science (WG 2020

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

Observation of Excess J/ψ Yield at Very Low Transverse Momenta in Au+Au Collisions at sqrt[s_{NN}]=200 GeV and U+U Collisions at sqrt[s_{NN}]=193 GeV.

We report on the first measurements of J/ψ production at very low transverse momentum (p_{T}<0.2  GeV/c) in hadronic Au+Au collisions at sqrt[s_{NN}]=200  GeV and U+U collisions at sqrt[s_{NN}]=193  GeV. Remarkably, the inferred nuclear modification factor of J/ψ at midrapidity in Au+Au (U+U) collisions reaches about 24 (52) for p_{T}<0.05  GeV/c in the 60%-80% collision centrality class. This noteworthy enhancement cannot be explained by hadronic production accompanied by cold and hot medium effects. In addition, the dN/dt distribution of J/ψ for the very low p_{T} range is presented for the first time. The distribution is consistent with that expected from the Au nucleus and shows a hint of interference. Comparison of the measurements to theoretical calculations of coherent production shows that the excess yield can be described reasonably well and reveals a partial disruption of coherent production in semicentral collisions, perhaps due to the violent hadronic interactions. Incorporating theoretical calculations, the results strongly suggest that the dramatic enhancement of J/ψ yield observed at extremely low p_{T} originates from coherent photon-nucleus interactions. In particular, coherently produced J/ψ's in violent hadronic collisions may provide a novel probe of the quark-gluon plasma

Longitudinal double-spin asymmetry for inclusive jet and dijet production in pp collisions at s =510 GeV

We report the first measurement of the inclusive jet and the dijet longitudinal double-spin asymmetries, ALL, at midrapidity in polarized pp collisions at a center-of-mass energy s=510 GeV. The inclusive jet ALL measurement is sensitive to the gluon helicity distribution down to a gluon momentum fraction of x≈0.015, while the dijet measurements, separated into four jet-pair topologies, provide constraints on the x dependence of the gluon polarization. Both results are consistent with previous measurements made at s=200 GeV in the overlapping kinematic region, x>0.05, and show good agreement with predictions from recent next-to-leading order global analyses