Importance of single author papers? I'm a fourth year PhD student in theoretical computer science. I'd like to stay in academia, so I'm thinking about how best to advance my career. Obviously the best way to do that is write lots of good papers, but another question is whether I should be trying to have more of those papers be single author.

So far I only have one single author paper (out of six). It's neither my best work, nor very recent. Is that a red flag when applying for postdoc or faculty positions? Should I try to have more single author papers?

This comes down to my approach to research. I like talking to people. I like telling people what I'm working on and, if they are interested, I'm keen to work with them. In other words, I'm very open to collaboration even when it isn't strictly necessary. Should I change that? That is, should I try to keep projects to myself more so that I end up with some single author papers?

Apologies if this question is off topic. I want to ask this question to people in my area, rather than on a general forum like academia.se. In particular, on all my papers, authors are ordered alphabetically. This makes single author papers a more important signal in TCS than in other areas, where author ordering conveys this information.
In some fields (like e.g. Economics and Mathematics) single authored papers -are- a good thing to have when you go on the job market. In theoretical computer science, collaboration is much more common, and it is not unusual for even relatively senior researchers to have very few single authored papers. It is not at all suspicious if a student on the market has only papers with co-authors. This is partly because we publish more frequently, so it is ok that each individual paper has less signal about your specific contribution. This is not to say that single authored papers are not impressive, but credit is super-additive across authors, and all things being equal, you should prefer to have a better paper with more coauthors than a worse paper with fewer. This should push you towards collaboration, since collaborators make your research both more fun and generally stronger. 

Of course in hiring decisions, committees will attempt to figure out whether you were a significant contributor to the papers you worked on or not -- but this will be done largely through the letters you obtain. If you have several good papers with the same senior co-author, that coauthor should write a letter for you, since they can explain in detail your contribution. It also helps if you have a clear research agenda of your own. Many papers on -your- topic with a rotating cast of coauthors conveys that you are leading the research direction, in contrast to a series of papers on disparate topics, each in the research agenda of your various coauthors.