• Thumbnail for Directed acyclic graph
    mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists...
    45 KB (5,646 words) - 17:54, 7 June 2025
  • Thumbnail for Acyclic orientation
    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...
    9 KB (1,081 words) - 19:18, 2 November 2024
  • Thumbnail for Orientation (graph theory)
    An acyclic orientation is an orientation that results in a directed acyclic graph. Every graph has an acyclic orientation; all acyclic orientations may...
    8 KB (961 words) - 04:21, 21 June 2025
  • Thumbnail for Strong orientation
    produces an acyclic orientation) then the acyclic orientation formed by reversing st is a bipolar orientation. Every bipolar orientation is related to...
    16 KB (1,858 words) - 22:08, 17 February 2025
  • 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...
    4 KB (520 words) - 04:14, 15 December 2023
  • Thumbnail for Bipolar orientation
    a directed graph. It is an acyclic orientation if the resulting directed graph has no directed cycles. Every acyclically oriented graph has at least...
    15 KB (1,839 words) - 20:42, 19 January 2025
  • Thumbnail for Gallai–Hasse–Roy–Vitaver theorem
    minimum length always include at least one acyclic orientation. This theorem implies that every orientation of a graph with chromatic number k {\displaystyle...
    16 KB (1,754 words) - 11:46, 18 June 2025
  • When the orientation has the additional property that the orientation forms a directed acyclic graph, which happens when unique sink orientations are used...
    6 KB (754 words) - 18:09, 4 January 2024
  • Thumbnail for Chromatic polynomial
    ) | V ( G ) | {\displaystyle (-1)^{|V(G)|}} times the number of acyclic orientations of G. The derivative evaluated at 1, P ′ ( G , 1 ) {\displaystyle...
    29 KB (4,324 words) - 10:57, 5 July 2025
  • directed acyclic graph, apply transitive closure, and remove orientation. Equivalently, a comparability graph is a graph that has a transitive orientation, an...
    13 KB (1,398 words) - 07:00, 10 May 2025
  • Thumbnail for Moral graph
    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...
    3 KB (400 words) - 00:26, 18 November 2024
  • Thumbnail for Polytree
    Polytree (category Directed acyclic graphs)
    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...
    8 KB (852 words) - 06:20, 9 May 2025
  • orientation include tournaments, orientations of complete graphs; strong orientations, orientations that are strongly connected; acyclic orientations...
    109 KB (16,011 words) - 12:09, 30 June 2025
  • Thumbnail for Tree (graph theory)
    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...
    27 KB (3,383 words) - 16:48, 14 March 2025
  • Thumbnail for Graph coloring
    {\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...
    70 KB (8,460 words) - 16:34, 7 July 2025
  • Thumbnail for Dual graph
    strongly connected graph) are dual to acyclic orientations (assignments of directions that produce a directed acyclic graph). In the same way, dijoins (sets...
    51 KB (6,607 words) - 00:16, 3 April 2025
  • {\displaystyle G} with n {\displaystyle n} available colors. For an acyclic orientation σ {\displaystyle \sigma } of the edges of G {\displaystyle G} , there...
    8 KB (1,272 words) - 17:21, 20 March 2024
  • Thumbnail for Tutte polynomial
    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 ...
    39 KB (5,377 words) - 15:46, 10 April 2025
  • Thumbnail for Directed graph
    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...
    16 KB (1,937 words) - 05:02, 12 April 2025
  • Thumbnail for Geometric graph theory
    Many important families of combinatorial structures, such as the acyclic orientations of a graph or the adjacencies between regions in a hyperplane arrangement...
    7 KB (934 words) - 20:16, 2 December 2024
  • Thumbnail for Graph (discrete mathematics)
    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...
    28 KB (3,671 words) - 04:30, 15 May 2025
  • Thumbnail for Homopolar generator
    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...
    19 KB (2,328 words) - 19:57, 12 January 2025
  • Thumbnail for Cis–trans isomerism
    Cis–trans isomerism (category Orientation (geometry))
    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...
    16 KB (1,738 words) - 15:38, 30 June 2025
  • Thumbnail for Heterocyclic compound
    electronic structure. The saturated organic heterocycles behave like the acyclic derivatives. Thus, piperidine and tetrahydrofuran are conventional amines...
    20 KB (1,151 words) - 06:14, 7 July 2025
  • 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...
    4 KB (599 words) - 07:56, 18 August 2023
  • Thumbnail for Degeneracy (graph theory)
    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...
    31 KB (3,769 words) - 02:53, 17 March 2025
  • Thumbnail for Asymmetric induction
    that 1,3-stereocontrol is possible if the reaction proceeds through an acyclic transition state. The reaction of β-alkoxy aldehyde with allyltrimethylsilane...
    29 KB (3,695 words) - 13:28, 30 January 2025
  • Thumbnail for Xylose
    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...
    9 KB (866 words) - 19:05, 4 May 2025
  • one-to-one. Undirected graphs of bounded genus, bounded degree, or bounded acyclic chromatic number also have bounded oriented chromatic number. Sopena wrote...
    4 KB (558 words) - 15:09, 11 March 2024
  • 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...
    13 KB (2,063 words) - 06:45, 17 October 2024