In mathematics, and more specifically in graph theory, a polytree (also called directed tree, oriented tree or singly connected network) is a directed...

equivalently a disjoint union of trees. A directed tree, oriented tree, polytree, or singly connected network is a directed acyclic graph (DAG) whose underlying...

acyclic undirected graph, or equivalently a disjoint union of trees. A polytree (or directed tree or oriented tree or singly connected network) is a directed...

tree. A polytree (also called a directed tree) is a multitree formed by orienting the edges of an undirected tree. An arborescence is a polytree formed...

single edge. Orientations of trees are always acyclic, and give rise to polytrees. Acyclic orientations of complete graphs are called transitive tournaments...

}}\leq 2{\frac {3}{11}}} , and it is conjectured that the limit is 2. A polytree, a directed acyclic graph formed by orienting the edges of an undirected...

A polytree is an orientation of an undirected tree. Sumner's conjecture states that every tournament with 2n – 2 vertices contains every polytree with...

any directed cycles Forest (graph theory), an undirected acyclic graph Polytree, a directed graph without any undirected cycles This disambiguation page...

formulated it as an exact inference algorithm on trees, later extended to polytrees. While the algorithm is not exact on general graphs, it has been shown...

that can be drawn in the plane with at most k crossings per edge. polytree A polytree is an oriented tree; equivalently, a directed acyclic graph whose...

tournaments are universal for polytrees, in the sense that every tournament with 2n − 2 vertices contains every polytree with n vertices as a subgraph...

tree Free tree Game tree K-ary tree Octree Parse tree Phylogenetic tree Polytree Positional tree PQ tree R-tree Rooted tree Ordered tree Recursive tree...

graphs for polytrees. The conjecture was proven for all large n {\displaystyle n} by Daniela Kühn, Richard Mycroft, and Deryk Osthus. Let polytree P {\displaystyle...

the same starting vertex to the same ending vertex. Oriented trees or polytrees are DAGs formed by orienting the edges of trees (connected, acyclic undirected...

space (technically a simply connected domain), the Reeb graph forms a polytree and is also called a contour tree. Level set graphs help statistical inference...

statement can be generalized from paths to other directed graphs: for every polytree P {\displaystyle P} there is a dual directed graph D {\displaystyle D}...

Mixture distribution Mixture model Naive Bayes classifier Plate notation Polytree Sensor fusion Sequence alignment Structural equation modeling Subjective...

blanket – Subset of variables that contains all the useful information Polytree – directed acyclic graph whose underlying undirected graph is a treePages...

and rational function modeling Polynomial chaos Polynomial regression Polytree (Bayesian networks) Pooled standard deviation – redirects to Pooled variance...

co-authors published a proof of Sumner's conjecture, that "every n-vertex polytree forms a subgraph of every (2n − 2)-vertex tournament", for all but finitely...

formulated Sumner's conjecture that tournaments are universal graphs for polytrees in 1971, and showed in 1974 that all claw-free graphs with an even number...

340282366920938463463374607431768211457, ... Fn = 22n + 1 for n ≥ 0. A000215 Polytrees 1, 1, 3, 8, 27, 91, 350, 1376, 5743, 24635, 108968, ... Number of oriented...

orders and partial orders whose Hasse diagram is N-free, semiorders. and polytrees. In the limit as n goes to infinity, the proportion of n-element partial...