21,003 research outputs found

    Long cycles in graphs with large degree sums and neighborhood unions

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    We present and prove several results concerning the length of longest cycles in 2-connected or 1-tough graphs with large degree sums. These results improve many known results on long cycles in these graphs. We also consider the sharpness of the results and discuss some possible strengthenings

    The Complexity of Change

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    Many combinatorial problems can be formulated as "Can I transform configuration 1 into configuration 2, if certain transformations only are allowed?". An example of such a question is: given two k-colourings of a graph, can I transform the first k-colouring into the second one, by recolouring one vertex at a time, and always maintaining a proper k-colouring? Another example is: given two solutions of a SAT-instance, can I transform the first solution into the second one, by changing the truth value one variable at a time, and always maintaining a solution of the SAT-instance? Other examples can be found in many classical puzzles, such as the 15-Puzzle and Rubik's Cube. In this survey we shall give an overview of some older and more recent work on this type of problem. The emphasis will be on the computational complexity of the problems: how hard is it to decide if a certain transformation is possible or not?Comment: 28 pages, 6 figure

    Long cycles in graphs containing a 2-factor with many odd components

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    We prove a result on the length of a longest cycle in a graph on n vertices that contains a 2-factor and satisfies d(u)+d(c)+d(w)n+2 for every tiple u, v, w of independent vertices. As a corollary we obtain the follwing improvement of a conjectre of Häggkvist (1992): Let G be a 2-connected graph on n vertices where every pair of nonadjacent vertices has degree sum at least n-k and assume G has a 2-factor with at least k+1 odd components. Then G is hamiltonian

    Algorithmic aspects of a chip-firing game

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    Algorithmic aspects of a chip-firing game on a graph introduced by Biggs are studied. This variant of the chip-firing game, called the dollar game, has the properties that every starting configuration leads to a so-called critical configuration. The set of critical configurations has many interesting properties. In this paper it is proved that the number of steps needed to reach a critical configuration is polynomial in the number of edges of the graph and the number of chips in the starting configuration, but not necessarily in the size of the input. An alternative algorithm is also described and analysed

    Pancyclicity of Hamiltonian line graphs

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    Let f(n) be the smallest integer such that for every graph G of order n with minimum degree 3(G)>f(n), the line graph L(G) of G is pancyclic whenever L(G) is hamiltonian. Results are proved showing that f(n) = ®(n 1/3)

    Formation of Double Neutron Stars, Millisecond Pulsars and Double Black Holes

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    The 1982 model for the formation of the Hulse-Taylor binary radio pulsar PSR B1913+16 is described, which since has become the standard model for the formation of double neutron stars, confirmed by the 2003 discovery of the double pulsar system PSR J0737-3039AB. A brief overview is given of the present status of our knowledge of the double neutron stars, of which 15 systems are presently known. The binary-recycling model for the formation of millisecond pulsars is described, as put forward independently by Alpar et al. (1982), Radhakrishnan and Srinivasan (1982) and Fabian et al. (1983). This now is the standard model for the formation of these objects, confirmed by the discovery in 1998 of the accreting millisecond X-ray pulsars. It is noticed that the formation process of close double black holes has analogies to that of close double neutron stars, extended to binaries of larger iinitial component masses, although there are also considerable differences in the physics of the binary evolution at these larger masses.Comment: Has appeared in Journal of Astrophysics and Astronomy special issue on 'Physics of Neutron Stars and Related Objects', celebrating the 75th birth year of G. Srinivasa

    Formation of the Galactic Millisecond Pulsar Triple System PSR J0337+1715 - a Neutron Star with Two Orbiting White Dwarfs

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    The millisecond pulsar in a triple system (PSR J0337+1715, recently discovered by Ransom et al.) is an unusual neutron star with two orbiting white dwarfs. The existence of such a system in the Galactic field poses new challenges to stellar astrophysics for understanding evolution, interactions and mass-transfer in close multiple stellar systems. In addition, this system provides the first precise confirmation for a very wide-orbit system of the white dwarf mass-orbital period relation. Here we present a self-consistent, semi-analytical solution to the formation of PSR J0337+1715. Our model constrains the peculiar velocity of the system to be less than 160 km/s and brings novel insight to, for example, common envelope evolution in a triple system, for which we find evidence for in-spiral of both outer stars. Finally, we briefly discuss our scenario in relation to alternative models.Comment: ApJ Letters, in press (6 pages, 3 figures, 1 table

    Co-combustion of Miscanthus in a pulverised coal combustor: Experiments in a droptube furnace

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    In this study, the devolatilisation process of Miscanthus particles inside a pulverised coal combustion chamber is characterised with the aim of finding conditions for which the devolatilisation rate of coal and Miscanthus is similar. However, choosing a power station as an experimental set-up for research is awkward because of the scale of operation (> 500 MWel). Therefore, BTG has designed and constructed a droptube reactor for well-controlled Miscanthus devolatilisation experiments with operational conditions that resemble those of a pulverised coal combustor. The droptube reactor has an internal diameter of 0.050 m and a maximum heated length of 1.6 m. Parameters which have been varied are: the droptube temperature (1000°, 1200°, 1300°, 1400°C); the heated droptube length (0.4, 0.8, 1.2, 1.6 m); and the particle size or sieve fraction (0.6¿1, 1¿2, 2¿2.8 mm). For a droptube length of 1.6 m, this results in a particle residence time of approximately 1 s.\ud \ud The experimental study on high-temperature Miscanthus decomposition in the droptube showed that Miscanthus particles which belong to the smallest sieve fraction (0.6¿1 mm) could be devolatilised completely in a 1.6 m long droptube. Apart from the experimental investigation, a numerical model has been developed. Samples of Miscanthus particles, representing grass-/straw-like crops, have been characterised in detail with respect to their size distribution. These data have been used to validate the numerical model with the results from the droptube experiments. The validation was successful. The model was then applied to predict the Miscanthus devolatilisation behaviour in a pulverised coal power station. The model predicts full conversion of Miscanthus particles for particles with a diameter smaller than 3 mm, in the core of the coal flame. Feeding of Miscanthus particles with a diameter up to 3 mm can therefore be recommended. Miscanthus particles with a diameter larger than 3 mm contribute to a geometrical extension of the coal flame in the upward direction. This should be avoided and firing of such large particles in a pulverised coal combustor is discouraged
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