Search results
Results from the WOW.Com Content Network
An Eulerian trail, [note 1] or Euler walk, in an undirected graph is a walk that uses each edge exactly once. If such a walk exists, the graph is called traversable or semi-eulerian. [3] An Eulerian cycle, [note 1] also called an Eulerian circuit or Euler tour, in an undirected graph is a cycle that uses each edge exactly once
[1] [2] The first appearance of this graph was in a paper as an example of a non-Hamiltonian, tough graph. [6] Douglas Shaw proved it to be minimal by showing all Eulerian graphs of order 6 or lower were not Hamiltonian and tough. Java code written by Shubhra Mishra and Marco Troper proved it unique. [2]
All Eulerian circuits are also Eulerian paths, but not all Eulerian paths are Eulerian circuits. Euler's work was presented to the St. Petersburg Academy on 26 August 1735, and published as Solutio problematis ad geometriam situs pertinentis (The solution of a problem relating to the geometry of position) in the journal Commentarii academiae ...
This tour corresponds to a Hamiltonian cycle in the line graph L(G), so the line graph of every Eulerian graph is Hamiltonian. Line graphs may have other Hamiltonian cycles that do not correspond to Euler tours, and in particular the line graph L(G) of every Hamiltonian graph G is itself Hamiltonian, regardless of whether the graph G is ...
Euler diagram illustrating that the set of "animals with four legs" is a subset of "animals", but the set of "minerals" is a disjoint set (it has no members in common) with "animals" Euler diagram showing the relationships between different Solar System objects
The Eulerian specification of the flow field is a way of looking at fluid motion that focuses on specific locations in the space through which the fluid flows as time passes. [ 1 ] [ 2 ] This can be visualized by sitting on the bank of a river and watching the water pass the fixed location.
Fleischner’s research focuses mainly on graph theoretical topics such as hamiltonian and eulerian graphs. One of his main achievements is the proof of the theorem according to which the square of every two-connected graph has a Hamiltonian cycle. This result (now known as Fleischner's theorem) had been submitted in 1971 and was published in 1974.
In the mathematical field of graph theory, the Meredith graph is a 4-regular undirected graph with 70 vertices and 140 edges discovered by Guy H. J. Meredith in 1973. [1]The Meredith graph is 4-vertex-connected and 4-edge-connected, has chromatic number 3, chromatic index 5, radius 7, diameter 8, girth 4 and is non-Hamiltonian. [2]