Graphs with the strong Havel-Hakimi property

The Havel-Hakimi algorithm iteratively reduces the degree sequence of a graph to a list of zeroes. As shown by Favaron, Mah\'eo, and Sacl\'e, the number of zeroes produced, known as the residue, is a lower bound on the independence number of the graph. We say that a graph has the strong Havel-Hakimi property if in each of its induced subgraphs, deleting any vertex of maximum degree reduces the degree sequence in the same way that the Havel-Hakimi algorithm does. We characterize graphs having this property (which include all threshold and matrogenic graphs) in terms of minimal forbidden induced subgraphs. We further show that for these graphs the residue equals the independence number, and a natural greedy algorithm always produces a maximum independent set.Comment: 7 pages, 3 figure

Flavor ordering of elliptic flows at high transverse momentum

Based on the quark coalescence model for the parton-to-hadron phase transition in ultra-relativistic heavy ion collisions, we relate the elliptic flow ($v_2$) of high \pt hadrons to that of high \pt quarks. For high \pt hadrons produced from an isospin symmetric and quark-antiquark symmetric partonic matter, magnitudes of their elliptic flows follow a flavor ordering as $(v_{2,\pi}=v_{2,N}) > (v_{2,\Lambda}=v_{2,\Sigma}) > v_{2,K} > v_{2,\Xi} > (v_{2,\phi}=v_{2,\Omega})$ if strange quarks have a smaller elliptic flow than light quarks. The elliptic flows of high \pt hadrons further follow a simple quark counting rule if strange quarks and light quarks have same high \pt spectrum and coalescence probability.Comment: 4 pages, 1 figure, revte

Dissipative effects from transport and viscous hydrodynamics

We compare 2->2 covariant transport theory and causal Israel-Stewart hydrodynamics in 2+1D longitudinally boost invariant geometry with RHIC-like initial conditions and a conformal e = 3p equation of state. The pressure evolution in the center of the collision zone and the final differential elliptic flow v2(pT) from the two theories agree remarkably well for a small shear viscosity to entropy density ratio eta/s ~ 1/(4 pi), and also for a large cross section sigma ~ 50 mb. A key to this agreement is keeping ALL terms in the Israel-Stewart equations of motion. Our results indicate promising prospects for the applicability of Israel-Stewart dissipative hydrodynamics at RHIC, provided the shear viscosity of hot and dense quark-gluon matter is indeed very small for the relevant temperatures T ~ 200-500 MeV.Comment: Presentation at Quark Matter 2008. 4 pages, 3 figure

Differential freezeout and pion interferometry at RHIC from covariant transport theory

Puzzling discrepancies between recent pion interferometry data on Au+Au reactions at s^1/2 = 130 and 200 AGeV from RHIC and predictions based on ideal hydrodynamics are analyzed in terms of covariant parton transport theory. The discrepancies of out and longitudinal radii are significantly reduced when the finite opacity of the gluon plasma is taken into account.Comment: 4 pages, 3 EPS figures. Submitted to PR