In graph theory, an acyclic orientation of an undirected graph is an assignment of a direction to each edge (an orientation) that does not form any directed...

mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists...

An acyclic orientation is an orientation that results in a directed acyclic graph. Every graph has an acyclic orientation; all acyclic orientations may...

minimum length always include at least one acyclic orientation. This theorem implies that every orientation of a graph with chromatic number k {\displaystyle...

schedule for the disjunctive graph may be obtained by finding an acyclic orientation of the undirected edges – that is, deciding for each pair of non-simultaneous...

produces an acyclic orientation) then the acyclic orientation formed by reversing st is a bipolar orientation. Every bipolar orientation is related to...

When the orientation has the additional property that the orientation forms a directed acyclic graph, which happens when unique sink orientations are used...

orientation include tournaments, orientations of complete graphs; strong orientations, orientations that are strongly connected; acyclic orientations...

a directed graph. It is an acyclic orientation if the resulting directed graph has no directed cycles. Every acyclically oriented graph has at least...

{\displaystyle \Delta +1} . A graph has a k-coloring if and only if it has an acyclic orientation for which the longest path has length at most k; this is the...

connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected...

directed acyclic graph, apply transitive closure, and remove orientation. Equivalently, a comparability graph is a graph that has a transitive orientation, an...

{\displaystyle G} with n {\displaystyle n} available colors. For an acyclic orientation σ {\displaystyle \sigma } of the edges of G {\displaystyle G} , there...

) | V ( G ) | {\displaystyle (-1)^{|V(G)|}} times the number of acyclic orientations of G. The derivative evaluated at 1, P ′ ( G , 1 ) {\displaystyle...

directed tree, oriented tree or singly connected network) is a directed acyclic graph whose underlying undirected graph is a tree. In other words, if we...

moral graph is used to find the equivalent undirected form of a directed acyclic graph. It is a key step of the junction tree algorithm, used in belief...

on the direction of rotation and the orientation of the field. It is also known as a unipolar generator, acyclic generator, disk dynamo, or Faraday disc...

digraph. A directed graph is acyclic if it has no directed cycles. The usual name for such a digraph is directed acyclic graph (DAG). Multitrees are DAGs...

Many important families of combinatorial structures, such as the acyclic orientations of a graph or the adjacencies between regions in a hyperplane arrangement...

strongly connected graph) are dual to acyclic orientations (assignments of directions that produce a directed acyclic graph). In the same way, dijoins (sets...

the number of acyclic orientations of G. T G ( 0 , 2 ) {\displaystyle T_{G}(0,2)} counts the number of strongly connected orientations of G. T G ( 2 ...

connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected...

Rastislav; Ružička, Peter (1999). "Rank of Graphs: The Size of Acyclic Orientation Cover for Deadlock-Free Packet Routing". SIROCCO 6. Proceedings of...

edges of G can be oriented to form a directed acyclic graph with outdegree at most k. Such an orientation can be formed by orienting each edge towards...

sink ( G , s ) {\displaystyle {\text{sink}}(G,s)} be the number of acyclic orientations on the graph G {\displaystyle G} which contain exactly s {\displaystyle...

called acyclic if Hj(X,E) = 0 for all j > 0. By the long exact sequence of sheaf cohomology, the cohomology of any sheaf can be computed from any acyclic resolution...

within a cyclohexane ring to prefer the axial orientation instead of the less-hindered equatorial orientation that would be expected from steric considerations...

electronic structure. The saturated organic heterocycles behave like the acyclic derivatives. Thus, piperidine and tetrahydrofuran are conventional amines...

Fischer projection is a systematic way of drawing the skeletal formula of an acyclic monosaccharide so that the handedness of each chiral carbon is well specified...

graph is not already a directed acyclic graph, a set of edges is identified the reversal of which will make it acyclic. Finding the smallest possible set...