1,404 research outputs found
Dichotomies properties on computational complexity of S-packing coloring problems
This work establishes the complexity class of several instances of the
S-packing coloring problem: for a graph G, a positive integer k and a non
decreasing list of integers S = (s\_1 , ..., s\_k ), G is S-colorable, if its
vertices can be partitioned into sets S\_i , i = 1,... , k, where each S\_i
being a s\_i -packing (a set of vertices at pairwise distance greater than
s\_i). For a list of three integers, a dichotomy between NP-complete problems
and polynomial time solvable problems is determined for subcubic graphs.
Moreover, for an unfixed size of list, the complexity of the S-packing coloring
problem is determined for several instances of the problem. These properties
are used in order to prove a dichotomy between NP-complete problems and
polynomial time solvable problems for lists of at most four integers
S-Packing Colorings of Cubic Graphs
Given a non-decreasing sequence of positive
integers, an {\em -packing coloring} of a graph is a mapping from
to such that any two vertices with color
are at mutual distance greater than , . This paper
studies -packing colorings of (sub)cubic graphs. We prove that subcubic
graphs are -packing colorable and -packing
colorable. For subdivisions of subcubic graphs we derive sharper bounds, and we
provide an example of a cubic graph of order which is not
-packing colorable
A characterization of b-chromatic and partial Grundy numbers by induced subgraphs
Gy{\'a}rf{\'a}s et al. and Zaker have proven that the Grundy number of a
graph satisfies if and only if contains an induced
subgraph called a -atom.The family of -atoms has bounded order and
contains a finite number of graphs.In this article, we introduce equivalents of
-atoms for b-coloring and partial Grundy coloring.This concept is used to
prove that determining if and (under
conditions for the b-coloring), for a graph , is in XP with parameter .We
illustrate the utility of the concept of -atoms by giving results on
b-critical vertices and edges, on b-perfect graphs and on graphs of girth at
least
Subdivision into i-packings and S-packing chromatic number of some lattices
An -packing in a graph is a set of vertices at pairwise distance
greater than . For a nondecreasing sequence of integers
, the -packing chromatic number of a graph is
the least integer such that there exists a coloring of into colors
where each set of vertices colored , , is an -packing.
This paper describes various subdivisions of an -packing into -packings
(j\textgreater{}i) for the hexagonal, square and triangular lattices. These
results allow us to bound the -packing chromatic number for these graphs,
with more precise bounds and exact values for sequences ,
Constraints on the location of a possible 9th planet derived from the Cassini data
To explain the unusual distribution of Kuiper Belt objects, several authors
have advocated the existence of a super-Earth planet in the outer solar system.
It has recently been proposed that a 10 M object with an orbit of
700 AU semi major axis and 0.6 eccentricity can explain the observed
distribution of Kuiper Belt objects around Sedna. Here we use the INPOP
planetary ephemerides model as a sensor for testing for an additional body in
the solar system. We test the possibility of adding the proposed planet without
increasing the residuals of the planetary ephemerides, fitted over the whole
INPOP planetary data sample. We demonstrate that the presence of such an object
is not compatible with the most sensitive data set, the Cassini radio ranging
data, if its true anomaly is in the intervals or
. Moreover, we find that the addition of this object
can reduce the Cassini residuals, with a most probable position given by a true
anomaly .Comment: Accepted for publication in A&A; 4 pages, 6 figure
Forecasting world and regional aviation Jet-Fuel demands to the mid term (2025).
This article provides jet fuel demand projections at the worldwide level and for eight geographical zones until 2025. Air traffic forecasts are performed using dynamic panel-data econometrics. Then, the conversion of air traffic projections into quantities of jet fuel is accomplished by using a complementary approach to the ‘Traffic Efficiency’ method developed previously by the UK Department of Trade and Industry to support the Intergovernmental Panel on Climate Change (IPCC, 1999). According to our main scenario, air traffic should increase by about 100% between 2008 and 2025 at the world level, corresponding to a yearly average growth rate of 4.7%. World jet fuel demand is expected to increase by about 38% during the same period, corresponding to a yearly average growth rate of 1.9% per year. According to these results, energy efficiency improvements allow reducing the effect of air traffic rise on the increase in jet fuel demand, but do not annihilate it. Jet fuel demand is thus unlikely to diminish unless there is a radical technological shift, or air travel demand is restricted.Energy efficiency; Jet fuel demand forecasts; Macro-level methodology;
- …