7 research outputs found
Independent sets and non-augmentable paths in generalizations of tournaments
AbstractWe study different classes of digraphs, which are generalizations of tournaments, to have the property of possessing a maximal independent set intersecting every non-augmentable path (in particular, every longest path). The classes are the arc-local tournament, quasi-transitive, locally in-semicomplete (out-semicomplete), and semicomplete k-partite digraphs. We present results on strongly internally and finally non-augmentable paths as well as a result that relates the degree of vertices and the length of longest paths. A short survey is included in the introduction
Independent sets and non-augmentable paths in arc-locally in-semicomplete digraphs and quasi-arc-transitive digraphs
AbstractA digraph is arc-locally in-semicomplete if for any pair of adjacent vertices x,y, every in-neighbor of x and every in-neighbor of y either are adjacent or are the same vertex. A digraph is quasi-arc-transitive if for any arc xy, every in-neighbor of x and every out-neighbor of y either are adjacent or are the same vertex. Laborde, Payan and Xuong proposed the following conjecture: Every digraph has an independent set intersecting every non-augmentable path (in particular, every longest path). In this paper, we shall prove that this conjecture is true for arc-locally in-semicomplete digraphs and quasi-arc-transitive digraphs
On the existence and number of -kings in -quasi-transitive digraphs
Let be a digraph and an integer. We say that
is -quasi-transitive if for every directed path in
, then or . Clearly, a
2-quasi-transitive digraph is a quasi-transitive digraph in the usual sense.
Bang-Jensen and Gutin proved that a quasi-transitive digraph has a 3-king
if and only if has a unique initial strong component and, if has a
3-king and the unique initial strong component of has at least three
vertices, then has at least three 3-kings. In this paper we prove the
following generalization: A -quasi-transitive digraph has a -king
if and only if has a unique initial strong component, and if has a
-king then, either all the vertices of the unique initial strong
components are -kings or the number of -kings in is at least
.Comment: 17 page
Knowledge and Management Models for Sustainable Growth
In the last years sustainability has become a topic of global concern and a key issue in the strategic agenda of both business organizations and public authorities and organisations.
Significant changes in business landscape, the emergence of new technology, including social media, the pressure of new social concerns, have called into question established conceptualizations of competitiveness, wealth creation and growth.
New and unaddressed set of issues regarding how private and public organisations manage and invest their resources to create sustainable value have brought to light. In particular the increasing focus on environmental and social themes has suggested new dimensions to be taken into account in the value creation dynamics, both at organisations and communities level.
For companies the need of integrating corporate social and environmental responsibility issues into strategy and daily business operations, pose profound challenges, which, in turn, involve numerous processes and complex decisions influenced by many stakeholders. Facing these challenges calls for the creation, use and exploitation of new knowledge as well as the development of proper management models, approaches and tools aimed to contribute to the development and realization of environmentally and socially sustainable business strategies and practices