Problem
COM-B1-M09-P006 Even Number of Odd Degrees
#6
★★☆☆☆ Level 2 of 5
Prove that in every graph, the number of vertices of odd degree is even.
Split the degree sum into even and odd terms.
The sum of all degrees is \(2E\), so it is even. The sum of degrees of even-degree vertices is even. Hence the sum of degrees of odd-degree vertices is also even. A sum of an odd number of odd numbers would be odd, so the number of such vertices is even.
One of the key lemmas of the module.