8,428 research outputs found
Aggregate and Individual Price Adjustment
macroeconomics, price adjustment, wages, Keynes, rigidities
The Price of Connectivity for Vertex Cover
The vertex cover number of a graph is the minimum number of vertices that are
needed to cover all edges. When those vertices are further required to induce a
connected subgraph, the corresponding number is called the connected vertex
cover number, and is always greater or equal to the vertex cover number.
Connected vertex covers are found in many applications, and the relationship
between those two graph invariants is therefore a natural question to
investigate. For that purpose, we introduce the {\em Price of Connectivity},
defined as the ratio between the two vertex cover numbers. We prove that the
price of connectivity is at most 2 for arbitrary graphs. We further consider
graph classes in which the price of connectivity of every induced subgraph is
bounded by some real number . We obtain forbidden induced subgraph
characterizations for every real value .
We also investigate critical graphs for this property, namely, graphs whose
price of connectivity is strictly greater than that of any proper induced
subgraph. Those are the only graphs that can appear in a forbidden subgraph
characterization for the hereditary property of having a price of connectivity
at most . In particular, we completely characterize the critical graphs that
are also chordal.
Finally, we also consider the question of computing the price of connectivity
of a given graph. Unsurprisingly, the decision version of this question is
NP-hard. In fact, we show that it is even complete for the class , the class of decision problems that can be solved in polynomial
time, provided we can make queries to an NP-oracle. This paves the
way for a thorough investigation of the complexity of problems involving ratios
of graph invariants.Comment: 19 pages, 8 figure
A search for muon-catalysed dd fusion in a deuterated organic crystal
Summary in English.Bibliography: pages 82-83.The possibility of muon-catalysed dd fusion via a Vesman-type mechanism in an organic crystal of deuterated anthracene is considered. In order to test this possibility the production of muons by 200 Me V protons incident on a 1mm Pb target is investigated. Two experiments to search for evidence of muon-catalysed fusion in a cylindrical deuterated anthracene crystal (9 mm diameter by l20 mm length) are described. The results indicate, tentatively, a fusion rate of 0.2 - 1.1 per incident μ-
A combined HST/CFH12k/XMM survey of X-ray luminous clusters of galaxies at z~0.2
We describe a project to study a sample of X-ray luminous clusters of
galaxies at redshift z~0.2 at several scales (with HST/WFPC2 and CFHT/CFH12k)
and wavebands (optical and X-ray). The main aims of the project are (i) to
determine the mass profiles of the clusters on scales ranging from ~10 kpc/h to
>1.5 Mpc/h using weak and strong lensing, thereby testing theoretical
predictions of a ``universal mass profile'', and (ii) to calibrate the M_tot -
T_X relation in view of future application in the study of the evolution of the
cluster mass function at higher redshift.Comment: 4 pages, 2 figures, Proceedings of the XXth Moriond Astrophysics
Meeting ``Cosmological Physics with Gravitational Lensing'', J.-P. Kneib, Y.
Mellier, M. Moniez and J. Tran Thanh Van eds., 200
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