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

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...

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

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

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...

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

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

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

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

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

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...

is a directed acyclic graph whose underlying undirected graph is a tree. In other words, a polytree is formed by assigning an orientation to each edge...

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

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...

{\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...

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

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

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 ...

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...

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...

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...

15 Hz) than for cis (range: 0–12 Hz; typical: 8 Hz) isomers. Usually for acyclic systems trans isomers are more stable than cis isomers. This difference...

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

an st-planar graph is a bipolar orientation of a plane graph for which both the source and the sink of the orientation are on the outer face of the graph...

can be oriented to form a directed acyclic graph with outdegree at most k {\displaystyle k} . Such an orientation can be formed by orienting each edge...

that 1,3-stereocontrol is possible if the reaction proceeds through an acyclic transition state. The reaction of β-alkoxy aldehyde with allyltrimethylsilane...

conditions. With its free aldehyde group, it is a reducing sugar. The acyclic form of xylose has chemical formula HOCH 2(CH(OH))3CHO. The cyclic hemiacetal...

one-to-one. Undirected graphs of bounded genus, bounded degree, or bounded acyclic chromatic number also have bounded oriented chromatic number. Sopena wrote...

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...