If I have a graph whose vertices all have odd degree greater than 1, what is the maximum possible number of vertices if the graph has at most 14 edges?
My thought for this is basically that your best case for odd degree being greater than 1 is 3, so you could use $2E\geq3n$ By this, I assumed the answer was 9, but I've been told 8 is the correct answer. Any ideas?
As mentioned in the comments by Morgan Rodgers,
Observe that $n$ can not be odd. For if $n$ is odd, then $$3n=\text {odd number}$$ which is not possible in a graph as sum of degrees of all vertices should be an even number by hand-shaking lemma.
Thus $n=8$ and not $9$.