All Questions

Question: what can be said about the existence of $2k$ regular graphs, $1\lt k$ that have a $1$-factor and a $2$-factor? Provided their existence, what is/are the smallest for $k$? The graphs must be ...

What is the smallest 3-regular graph to have a unique perfect matching? With a large enough number of nodes, it is possible for a 3-regular graph to have no perfect matching (example can be seen in ...