177,558 research outputs found
On the non-existence of an R-labeling
We present a family of Eulerian posets which does not have any R-labeling.
The result uses a structure theorem for R-labelings of the butterfly poset.Comment: 6 pages, 1 figure. To appear in the journal Orde
Multi-Sided Boundary Labeling
In the Boundary Labeling problem, we are given a set of points, referred
to as sites, inside an axis-parallel rectangle , and a set of pairwise
disjoint rectangular labels that are attached to from the outside. The task
is to connect the sites to the labels by non-intersecting rectilinear paths,
so-called leaders, with at most one bend.
In this paper, we study the Multi-Sided Boundary Labeling problem, with
labels lying on at least two sides of the enclosing rectangle. We present a
polynomial-time algorithm that computes a crossing-free leader layout if one
exists. So far, such an algorithm has only been known for the cases in which
labels lie on one side or on two opposite sides of (here a crossing-free
solution always exists). The case where labels may lie on adjacent sides is
more difficult. We present efficient algorithms for testing the existence of a
crossing-free leader layout that labels all sites and also for maximizing the
number of labeled sites in a crossing-free leader layout. For two-sided
boundary labeling with adjacent sides, we further show how to minimize the
total leader length in a crossing-free layout
A Study on Topological Integer Additive Set-Labeling of Graphs
A set-labeling of a graph is an injective function , where is a finite set and a set-indexer of is a
set-labeling such that the induced function defined by
for every is also injective. Let be a graph and let be a
non-empty set. A set-indexer is called a topological
set-labeling of if is a topology of . An integer additive
set-labeling is an injective function ,
whose associated function is defined by
, where is the set of all
non-negative integers and is its power set. An
integer additive set-indexer is an integer additive set-labeling such that the
induced function defined by is also injective. In this paper, we extend the concepts of
topological set-labeling of graphs to topological integer additive set-labeling
of graphs.Comment: 16 pages, 7 figures, Accepted for publication. arXiv admin note: text
overlap with arXiv:1403.398
The interplay between societal concerns and the regulatory frame on GM crops in the European Union
Recapitulating how genetic modification technology and its agro-food
products aroused strong societal opposition in the European Union, this
paper demonstrates how this opposition contributed to shape the European
regulatory frame on GM crops. More specifically, it describes how this
opposition contributed to a de facto moratorium on the commercialization of new GM
crop events in the end of the nineties. From this period onwards, the
regulatory frame has been continuously revised in order to slow down further
erosion of public and market confidence. Various scientific and technical
reforms were made to meet societal concerns relating to the safety of GM
crops. In this context, the precautionary principle, environmental
post-market monitoring and traceability were adopted as ways to cope with
scientific uncertainties. Labeling, traceability, co-existence and public
information were installed in an attempt to meet the general public request
for more information about GM agro-food products, and the specific demand to
respect the consumers' and farmers' freedom of choice. Despite these
efforts, today, the explicit role of public participation and/or ethical
consultation during authorization procedures is at best minimal. Moreover,
no legal room was created to progress to an integral sustainability
evaluation during market procedures. It remains to be seen whether the
recent policy shift towards greater transparency about value judgments,
plural viewpoints and scientific uncertainties will be one step forward in
integrating ethical concerns more explicitly in risk analysis. As such, the
regulatory frame stands open for further interpretation, reflecting in
various degrees a continued interplay with societal concerns relating to GM
agro-food products. In this regard, both societal concerns and diversely
interpreted regulatory criteria can be inferred as signaling a request –
and even a quest – to render more explicit the broader-than-scientific
dimension of the actual risk analysis
A Characterisation of Weak Integer Additive Set-Indexers of Graphs
An integer additive set-indexer is defined as an injective function
such that the induced function defined by is also
injective. An integer additive set-indexer is said to be -uniform if
for all . An integer additive set-indexer is said
to be a weak integer additive set-indexer if for
all . In this paper, we study the characteristics of certain
graphs and graph classes which admit weak integer additive set-indexers.Comment: 12pages, 4 figures, arXiv admin note: text overlap with
arXiv:1311.085
A Creative Review on Integer Additive Set-Valued Graphs
For a non-empty ground set , finite or infinite, the {\em set-valuation}
or {\em set-labeling} of a given graph is an injective function , where is the power set of the set . A
set-indexer of a graph is an injective set-valued function such that the function defined by for
every is also injective, where is a binary operation on
sets. An integer additive set-indexer is defined as an injective function
such that the induced function
defined by is
also injective, where is the set of all non-negative integers.
In this paper, we critically and creatively review the concepts and properties
of integer additive set-valued graphs.Comment: 14 pages, submitted. arXiv admin note: text overlap with
arXiv:1312.7672, arXiv:1312.767
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