11,425 research outputs found
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 () 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
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
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