7,174 research outputs found
Partitioning Perfect Graphs into Stars
The partition of graphs into "nice" subgraphs is a central algorithmic
problem with strong ties to matching theory. We study the partitioning of
undirected graphs into same-size stars, a problem known to be NP-complete even
for the case of stars on three vertices. We perform a thorough computational
complexity study of the problem on subclasses of perfect graphs and identify
several polynomial-time solvable cases, for example, on interval graphs and
bipartite permutation graphs, and also NP-complete cases, for example, on grid
graphs and chordal graphs.Comment: Manuscript accepted to Journal of Graph Theor
Uniform hypergraphs containing no grids
A hypergraph is called an rĂr grid if it is isomorphic to a pattern of r horizontal and r vertical lines, i.e.,a family of sets {A1, ..., Ar, B1, ..., Br} such that AiâŠAj=BiâŠBj=Ď for 1â¤i<jâ¤r and {pipe}AiâŠBj{pipe}=1 for 1â¤i, jâ¤r. Three sets C1, C2, C3 form a triangle if they pairwise intersect in three distinct singletons, {pipe}C1âŠC2{pipe}={pipe}C2âŠC3{pipe}={pipe}C3âŠC1{pipe}=1, C1âŠC2â C1âŠC3. A hypergraph is linear, if {pipe}EâŠF{pipe}â¤1 holds for every pair of edges Eâ F.In this paper we construct large linear r-hypergraphs which contain no grids. Moreover, a similar construction gives large linear r-hypergraphs which contain neither grids nor triangles. For râĽ. 4 our constructions are almost optimal. These investigations are motivated by coding theory: we get new bounds for optimal superimposed codes and designs. Š 2013 Elsevier Ltd
On the structure of defects in the Fe7Mo6 -Phase
Topologically close packed phases, among them the -phase studied here,
are commonly considered as being hard and brittle due to their close packed and
complex structure. Nanoindentation enables plastic deformation and therefore
investigation of the structure of mobile defects in the -phase, which, in
contrast to grown-in defects, has not been examined yet. High resolution
transmission electron microscopy (HR-TEM) performed on samples deformed by
nanoindentation revealed stacking faults which are likely induced by plastic
deformation. These defects were compared to theoretically possible stacking
faults within the -phase building blocks, and in particular Laves phase
layers. The experimentally observed stacking faults were found resulting from
synchroshear assumed to be associated with deformation in the Laves-phase
building blocks
Phase diagram of a two-dimensional lattice gas model of a ramp system
Using Monte Carlo Simulation and fundamental measure theory we study the
phase diagram of a two-dimensional lattice gas model with a nearest neighbor
hard core exclusion and a next-to-nearest neighbors finite repulsive
interaction. The model presents two competing ranges of interaction and, in
common with many experimental systems, exhibits a low density solid phase,
which melts back to the fluid phase upon compression. The theoretical approach
is found to provide a qualitatively correct picture of the phase diagram of our
model system.Comment: 14 pages, 8 figures, uses RevTex
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