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The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees. The tree is viewed as a directed graph that contains two directed edges for each edge in the tree. The tree can then be represented as a Eulerian circuit of the directed graph, known as the Euler tour representation (ETR) of the tree
The first complete proof of this latter claim was published posthumously in 1873 by Carl Hierholzer. [1] This is known as Euler's Theorem: A connected graph has an Euler cycle if and only if every vertex has an even number of incident edges. The term Eulerian graph has two common meanings in graph theory. One meaning is a graph with an Eulerian ...
Leonhard Euler is credited of introducing both specifications in two publications written in 1755 [3] and 1759. [4] [5] Joseph-Louis Lagrange studied the equations of motion in connection to the principle of least action in 1760, later in a treaty of fluid mechanics in 1781, [6] and thirdly in his book Mécanique analytique. [5]
In combinatorial mathematics and theoretical computer science, heavy-light decomposition (also called heavy path decomposition) is a technique for decomposing a rooted tree into a set of paths. In a heavy path decomposition, each non-leaf node selects one "heavy edge", the edge to the child that has the greatest number of descendants (breaking ...
Form the subgraph of G using only the vertices of O: Construct a minimum-weight perfect matching M in this subgraph Unite matching and spanning tree T ∪ M to form an Eulerian multigraph Calculate Euler tour Here the tour goes A->B->C->A->D->E->A. Equally valid is A->B->C->A->E->D->A. Remove repeated vertices, giving the algorithm's output.
An Euler diagram (/ ˈ ɔɪ l ər /, OY-lər) is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining complex hierarchies and overlapping definitions. They are similar to another set diagramming technique, Venn diagrams. Unlike Venn diagrams, which show all possible relations between ...
This page was last edited on 10 April 2004, at 14:21 (UTC).; Text is available under the
Euler's partition theorem relating the product and series representations of the Euler function Π(1 − x n) Goldbach–Euler theorem, stating that sum of 1/(k − 1), where k ranges over positive integers of the form m n for m ≥ 2 and n ≥ 2, equals 1; Gram–Euler theorem