In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices). Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail that starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Königsberg problem in 1736. The problem can be stated mathematically like this: Given the graph in the image, is it possible to construct a path (or a cycle; i.e., a path starting and ending on the same vertex) that visits each edge exactly once? Euler proved that a necessary condition for the existence of Eulerian circuits is that all vertices in the graph have an even degree, and stated without proof that connected graphs with all vertices of even degree have an Eulerian circuit. The first complete proof of this latter claim was published posthumously in 1873 by Carl Hierholzer. This is known as Euler's Theorem: A connected graph has an Euler cycle if and only if every vertex has even degree. The term Eulerian graph has two common meanings in graph theory. One meaning is a graph with an Eulerian circuit, and the other is a graph with every vertex of even degree. These definitions coincide for connected graphs. For the existence of Eulerian trails it is necessary that zero or two vertices have an odd degree; this means the Königsberg graph is not Eulerian. If there are no vertices of odd degree, all Eulerian trails are circuits. If there are exactly two vertices of odd degree, all Eulerian trails start at one of them and end at the other. A graph that has an Eulerian trail but not an Eulerian circuit is called semi-Eulerian. (Wikipedia).
Eulerian Path - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Eulerian Path - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Counting Eulerian Paths - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Counting Eulerian Paths Solution - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Introduction to Euler Paths and Euler Circuits
This video introduces Euler paths and Euler circuits. mathispower4u.com
From playlist Graph Theory (Discrete Math)
In an Eulerian walk, all the edges are visited, but only once. These walks can be closed (a cycle, where the start and end nodes are the same node) or open. You can learn more about Mathematica on my Udemy course at https://www.udemy.com/mathematica/ PS! Wait until Udemy has a sale and
From playlist Introducing graph theory
Graph Theory: Euler Paths and Euler Circuits
This lesson explains Euler paths and Euler circuits. Several examples are provided. Site: http://mathispower4u.com
From playlist Graph Theory
Eulerian Path Solution - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
The Chinese Postman Problem (Introduction to Graph Theory)
This video covers Eulerian, Semi-Eulerian, and regular graphs in the Chinese Postman Problem as well as applications of graph theory. This was made for 3Blue1Brown's Summer of Math Exploration video competition (link: https://www.3blue1brown.com/blog/some1). For more information about Eu
From playlist Summer of Math Exposition Youtube Videos
riding every amusement park ride in the shortest possible time
#SoME2 #maths #computerscience Have you ever wanted to optimize your route through an amusement park so that you hit every single ride in the shortest time possible? In this video we go over a famous problem in optimization in mathematics and computer science, the Traveling Salesman Pro
From playlist Summer of Math Exposition 2 videos
Solving Laplacian Systems of Directed Graphs - John Peebles
Computer Science/Discrete Mathematics Seminar II Topic: Solving Laplacian Systems of Directed Graphs Speaker: John Peebles Affiliation: Member, School of Mathematics Date: March 02, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
How the Königsberg bridge problem changed mathematics - Dan Van der Vieren
View full lesson: http://ed.ted.com/lessons/how-the-konigsberg-bridge-problem-changed-mathematics-dan-van-der-vieren You’d have a hard time finding the medieval city Königsberg on any modern maps, but one particular quirk in its geography has made it one of the most famous cities in mathe
From playlist New TED-Ed Originals
Engineering MAE 130A. Intro to Fluid Mechanics. Lecture 09.
UCI Engineering MAE 130A: Intro to Fluid Mechanics (Fall 2013) Lec 09. Intro to Fluid Mechanics View the complete course: http://ocw.uci.edu/courses/engineering_mae_130a_intro_to_fluid_mechanics.html Instructor: Roger Rangel, Ph.D. License: Creative Commons CC-BY-SA Terms of Use: http://o
From playlist Engineering MAE 130A. Intro to Fluid Mechanics
Ole Warnaar: Cylindric partitions and character identities
Abstract: As was shown in the 1980s by Kac, Peterson and Wakimoto, the characters of infinite dimensional Lie algebras provide a rich source of modular forms. Finding manifestly positive expressions for such characters remains, however, a difficult open problem. In this talk I will describ
From playlist Number Theory Down Under 9
Existence of Eulerian Paths and Circuits | Graph Theory
Explanation video on how to verify the existence of Eulerian Paths and Eulerian Circuits (also called Eulerian Trails/Tours/Cycles) Euler path/circuit algorithm: https://youtu.be/8MpoO2zA2l4 Euler path/circuit source code: https://youtu.be/QQ3jO1dKjYQ Algorithms repository: https://githu
From playlist Graph Theory Playlist
Create Graph With Eulerian Tour - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms