Pancyclicity of Hamiltonian line graphs

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)

The Complexity of Change

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 with large degree sums and neighborhood unions

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

Algorithmic aspects of a chip-firing game

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

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

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

On the complexity of the economic lot-sizing problem with remanufacturing options

In this paper we investigate the complexity of the economiclot-sizing problem with remanufacturing (ELSR) options. Whereas inthe classical economic lot-sizing problem demand can only besatisfied by production, in the ELSR problem demand can also besatisfied by remanufacturing returned items. Although the ELSRproblem can be solved efficiently for some special cases, we showthat the problem is NP-hard in general, even under stationary costparameters.remanufacturing;complexity;lot-sizing

The Welfare Cost of Bank Capital Requirements

Bank capital requirements, Welfare, Sidrauski model

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

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