Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $G = (V, E)$ be a graph with nine vertices, such that each vertex has degree $5$ or $6$. Show that $G$ has at least five vertices of degree $6$, or at least six vertices of degree $5$.

My friend and I have been working on this question for the past two days and we have nothing. Any pointers or help?

share|improve this question
4  
If neither of those things are true, $G$ has exactly $5$ vertices of degree $5$ and exactly $4$ vertices of degree $6$. Can you see why this is impossible? –  Micah May 11 '13 at 19:39
    
Oh my goodness, thank you. Both to Micah and Hagen. –  Evan May 11 '13 at 19:59
add comment

1 Answer 1

Hint: The sum of all vertex degrees is twice the number of edges.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.