Studying graphs and came across this theorem and wanted a quick clarification: http://www.math.toronto.edu/gscott/sept20_2016.pdf
Theorem: Let $G$ be a simple graph with $n$ vertices such that $n\geq{3}$. If every vertex has a degree of at least $n/2$, then $G$ has a hamiltonian cycle.
Does this theorem assume that $G$ is connected? or is this for any graph that meets the constraints?
If every vertices have degree at least n/2 then any 2 non-adjacent vertices must share a common adjacent vertex so connectedness is automatically implied.