Proof: Graph with all Even Degree Vertices has no Bridges | Graph Theory

A connected graph whose vertices all have even degree has no bridges! We will prove this result in today's graph theory lesson!

The proof follows pretty easily using contradiction, the definition of bridge, and some simple graph theory results we have previously proven. We'll use an argument about the parity (even or odd) of the sum of the degrees of the vertices in a subgraph of our graph.

Lesson on First Theorem of Graph Theory:    • The First Theorem of Graph Theory | G...  

Proof every graph has an even number of odd degree vertices:    • Proof: Every Graph has an Even Number...  

Lesson on bridges:    • What are Bridges of Graphs? | Graph T...  



I hope you find this video helpful, and be sure to ask any questions down in the comments!

********************************************************************
The outro music is by a friend of mine named Molly Ponkevitch, who, upon my request, kindly gave me permission to use her music in my outros. I usually put my own music in the outros, but I love Molly's music, and wanted to share it with those of you watching. Please check out her wonderful music and other work, as she also does poetry and more.

Molly's YouTube:    / @mollyponkevitch1512  
Molly's Instagram: https://www.instagram.com/dyx_soma/?h...
Molly's Website: https://www.mollyponkevitch.com/
********************************************************************

+WRATH OF MATH+

◆ Support Wrath of Math on Patreon:   / wrathofmathlessons  

Follow Wrath of Math on...
● Instagram:   / wrathofmathedu  
● Facebook:   / wrathofmath  
● Twitter:   / wrathofmathedu  

My Music Channel:    / seanemusic