20,379 research outputs found
Szemer\'edi's Regularity Lemma for matrices and sparse graphs
Szemer\'edi's Regularity Lemma is an important tool for analyzing the
structure of dense graphs. There are versions of the Regularity Lemma for
sparse graphs, but these only apply when the graph satisfies some local density
condition. In this paper, we prove a sparse Regularity Lemma that holds for all
graphs. More generally, we give a Regularity Lemma that holds for arbitrary
real matrices
The Parameterised Complexity of List Problems on Graphs of Bounded Treewidth
We consider the parameterised complexity of several list problems on graphs,
with parameter treewidth or pathwidth. In particular, we show that List Edge
Chromatic Number and List Total Chromatic Number are fixed parameter tractable,
parameterised by treewidth, whereas List Hamilton Path is W[1]-hard, even
parameterised by pathwidth. These results resolve two open questions of
Fellows, Fomin, Lokshtanov, Rosamond, Saurabh, Szeider and Thomassen (2011).Comment: Author final version, to appear in Information and Computation.
Changes from previous version include improved literature references and
restructured proof in Section
Flux surface shaping effects on tokamak edge turbulence and flows
Shaping of magnetic flux surfaces is found to have a strong impact on
turbulence and transport in tokamak edge plasmas. A series of axisymmetric
equilibria with varying elongation and triangularity, and a divertor
configuration are implemented into a computational gyrofluid turbulence model.
The mechanisms of shaping effects on turbulence and flows are identified.
Transport is mainly reduced by local magnetic shearing and an enhancement of
zonal shear flows induced by elongation and X-point shaping.Comment: 10 pages, 11 figures. Submitted to Physics of Plasma
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