# Category: Trees (graph theory)

Starlike tree
In the area of mathematics known as graph theory, a tree is said to be starlike if it has exactly one vertex of degree greater than 2. This high-degree vertex is the root and a starlike tree is obtain
Lowest common ancestor
In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest)
Random recursive tree
In probability theory, a random recursive tree is a rooted tree chosen uniformly at random from the recursive trees with a given number of vertices.
Arborescence (graph theory)
In graph theory, an arborescence is a directed graph in which, for a vertex u (called the root) and any other vertex v, there is exactly one directed path from u to v. An arborescence is thus the dire
Buchholz hydra
In mathematical logic, the Buchholz hydra game is a hydra game, which is a single-player game based on the idea of chopping pieces off a mathematical tree. The hydra game can be used to generate a rap
Recursive tree
In graph theory, a recursive tree (i.e., unordered tree) is a labeled, rooted tree. A size-n recursive tree's vertices are labeled by distinct positive integers 1, 2, …, n, where the labels are strict
Tree decomposition
In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the graph. Tree d
Prüfer sequence
In combinatorial mathematics, the Prüfer sequence (also Prüfer code or Prüfer numbers) of a labeled tree is a unique sequence associated with the tree. The sequence for a tree on n vertices has length
Steiner tree problem
In combinatorial mathematics, the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization. While Ste
Wedderburn–Etherington number
The Wedderburn–Etherington numbers are an integer sequence named for Ivor Malcolm Haddon Etherington and Joseph Wedderburn that can be used to count certain kinds of binary trees. The first few number
Branch-decomposition
In graph theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree T with the edges of G as its leaves. Removing an
Wiener connector
In network theory, the Wiener connector is a means of maximizing efficiency in connecting specified "query vertices" in a network. Given a connected, undirected graph and a set of query vertices in a
Game tree
In the context of Combinatorial game theory, which typically studies sequential games with perfect information, a game tree is a graph representing all possible game states within such a game. Such ga
Cayley's formula
In mathematics, Cayley's formula is a result in graph theory named after Arthur Cayley. It states that for every positive integer , the number of trees on labeled vertices is . The formula equivalentl
Tree (graph theory)
In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in whi
Path graph
In the mathematical field of graph theory, a path graph or linear graph is a graph whose vertices can be listed in the order v1, v2, …, vn such that the edges are {vi, vi+1} where i = 1, 2, …, n − 1.
M-ary tree
In graph theory, an m-ary tree (also known as n-ary, k-ary or k-way tree) is a rooted tree in which each node has no more than m children. A binary tree is the special case where m = 2, and a ternary
Variation (game tree)
A variation can refer to a specific sequence of successive moves in a turn-based game, often used to specify a hypothetical future state of a game that is being played. Although the term is most commo
Block graph
In graph theory, a branch of combinatorial mathematics, a block graph or clique tree is a type of undirected graph in which every biconnected component (block) is a clique. Block graphs are sometimes
Level ancestor problem
In graph theory and theoretical computer science, the level ancestor problem is the problem of preprocessing a given rooted tree T into a data structure that can determine the ancestor of a given node
Uniform tree
In mathematics, a uniform tree is a locally finite tree which is the universal cover of a finite graph. Equivalently, the full automorphism group G=Aut(X) of the tree, which is a locally compact topol
Bethe lattice
In statistical mechanics and mathematics, the Bethe lattice (also called a regular tree) is an infinite connected cycle-free graph where all vertices have the same number of neighbors. The Bethe latti
Serre's property FA
In mathematics, Property FA is a property of groups first defined by Jean-Pierre Serre. A group G is said to have property FA if every action of G on a tree has a global fixed point. Serre shows that
Centered tree
In the mathematical subfield of graph theory, a centered tree is a tree with only one center, and a bicentered tree is a tree with two centers. Given a graph, the eccentricity of a vertex v is defined
Rectilinear Steiner tree
The rectilinear Steiner tree problem, minimum rectilinear Steiner tree problem (MRST), or rectilinear Steiner minimum tree problem (RSMT) is a variant of the geometric Steiner tree problem in the plan
Unrooted binary tree
In mathematics and computer science, an unrooted binary tree is an unrooted tree in which each vertex has either one or three neighbors.
Random tree
In mathematics and computer science, a random tree is a tree or arborescence that is formed by a stochastic process. Types of random trees include: * Uniform spanning tree, a spanning tree of a given
K-tree
In graph theory, a k-tree is an undirected graph formed by starting with a (k + 1)-vertex complete graph and then repeatedly adding vertices in such a way that each added vertex v has exactly k neighb
Polytree
In mathematics, and more specifically in graph theory, a polytree (also called directed tree, oriented tree or singly connected network) is a directed acyclic graph whose underlying undirected graph i
Jordan–Pólya number
In mathematics, the Jordan–Pólya numbers are the numbers that can be obtained by multiplying together one or more factorials, not required to be distinct from each other. For instance, is a Jordan–Pól
Strahler number
In mathematics, the Strahler number or Horton–Strahler number of a mathematical tree is a numerical measure of its branching complexity. These numbers were first developed in hydrology by Robert E. Ho
Pfafstetter Coding System
The Pfafstetter Coding System is a hierarchical method of hydrologically coding river basins. It was developed by the Brazilian engineer in 1989. It is designed such that topological information is em
Hypertree
In the mathematical field of graph theory, a hypergraph H is called a hypertree if it admits a host graph T such that T is a tree. In other words, H is a hypertree if there exists a tree T such that e
Linear forest
In graph theory, a branch of mathematics, a linear forest is a kind of forest formed from the disjoint union of path graphs. It is an undirected graph with no cycles in which every vertex has degree a
Star (graph theory)
In graph theory, a star Sk is the complete bipartite graph K1,k : a tree with one internal node and k leaves (but no internal nodes and k + 1 leaves when k ≤ 1). Alternatively, some authors define Sk
Agreement forest
In the mathematical field of graph theory, an agreement forest for two given (leaf-labeled, irreductible) trees is any (leaf-labeled, irreductible) forest which can, informally speaking, be obtained f
Heavy path decomposition
In combinatorial mathematics and theoretical computer science, heavy path decomposition (also called heavy-light decomposition) is a technique for decomposing a rooted tree into a set of paths. In a h
Blossom tree (graph theory)
In the study of planar graphs, blossom trees are trees with additional directed half edges. Each blossom tree is associated with an embedding of a planar graph. Blossom trees can be used to sample ran
Kruskal's tree theorem
In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding.
Caterpillar tree
In graph theory, a caterpillar or caterpillar tree is a tree in which all the vertices are within distance 1 of a central path. Caterpillars were first studied in a series of papers by Harary and Schw