I begin by reviewing the proof that a graph has an Euler tour if and only if every vertex has even degree. Then I show a proof that a graph has an Euler trail if and only it has either 0 or 2 vertices of odd degree.
An introduction to Graph Theory by Dr. Sarada Herke.
Related Videos:
http://youtu.be/eIb1cz06UwI - Graph Theory: 01. Seven Bridges of Konigsberg
http://youtu.be/1V_6nUUNoms - Graph Theory: 23. Euler Trails and Euler Tours
http://youtu.be/YoRhmz_OSBY - Graph Theory: 06 Sum of Degrees is ALWAYS Twice the Number of Edges
For quick videos about Math tips and useful facts, check out my other channel
"Spoonful of Maths" -
http://youtube.com/spoonfulofmaths