I've been thinking about this particular problem and I'm stumped.
For all $n g\geq 5$, show that there exists a graph, $G = \langle V,E \rangle$ such that all vertices of $V$ have degree of $4$.
I've tried using Havel-Hakami with a degree sequence of n-fours (ie: $[4,4,4,4,4,4,\ldots]$), but there were too many cases. I can't think of anything else. Any suggestions or ideas?