Problem
COM-B2-M07-P002 Odd Degrees
#2
★★☆☆☆ Level 2 of 5
Prove that in every finite graph, the number of vertices of odd degree is even.
Use the parity of the degree sum.
The sum of degrees is \(2m\), 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 odd integers is even only when the number of summands is even.
A classic parity fact for Euler problems.