21,503 research outputs found
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
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 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
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
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)
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
Formation of the Galactic Millisecond Pulsar Triple System PSR J0337+1715 - a Neutron Star with Two Orbiting White Dwarfs
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
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
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