Question: Are there any good video lectures available on Analytic Number Theory? I have a decent background of complex analysis but I have just started Analytic Number Theory.

Answer: 
Use the representation of the $k$-cube as a binary vector of length $k$.
For each set of binary digits $b2,\ldots,b\_k$ you have an edge between
$(0,b\_2,\ldots,b\_k)$ and $(1,b\_2,\ldots,b\_k)$.

Now show that this constitutes a perfect matching.
For k cube graph, we have 2^k number of the vertex that is even number of vertex. now arrange all the vertex in a circle and number them according to grey code. so we will have a cycle of an even number of vertices with some interconnections in-between. and we know that we have perfect matching for a cycle with an even number of vertices, hence proved.