These four papers have all been published in journals within the past few months; I just now updated my online pub list and the arxiv metadata for them to match.

To keep this from being totally content-free, here's an unsolved graph theory problem from the last paper (I thought I'd posted this before, but now I can't find it, so...):

In that paper, there are matching $$2^{n/2}$$ upper and lower bounds on the number of Hamiltonian cycles in 3-regular multigraphs (the lower bound is formed by a cycle that alternates between single and double bonds). But for simple cubic graphs, the best bounds I have are a $$2^{3n/8}$$ upper bound, and a $$2^{n/3}$$ lower bound. I conjecture that the $$2^{n/3}$$ lower bound is tight. Can a matching upper bound be proven?