I am a senior PhD student in computer science. I have published several papers with my PhD advisor already.
Someone told me that, when applying for faculty positions, it looks good to have a peer-reviewed paper without your advisor listed as an author. I guess it implies that you can complete a solid project without someone holding your hand. Is this true?
The comments here seem to cover the ground pretty well. Having publications of any sort is a plus. Having lots of collaborations is a big plus and well serve you well in your future work, not just in applications.
But in some fields it is more or less necessary to have your advisor, and maybe others, on publications that arise from your dissertation work. In other fields that would be unusual.
However, don't obsess over this issue. Do the best work you can and publish the work as best you can with appropriate authorship for the work and for the field. After you finish the degree and become more independent of your advisor, you will probably write sole author papers. But if you have the opportunity for a sole author publication as a student, don't pass it up.
But don't neglect the synergistic power of collaboration in what you do.
If you only have papers with your PhD supervisor as a co-author, a selection commision may wonder about your academic independence; whether the underlying ideas are all yours or all have been fed to you by your advisor. Having a paper without you PhD supervisor (or other senior scientists) as co-authors, helps to alleviate these worries. That this is viewed as valuable can be seen from the fact that applications for ERC starting grants specifically ask the applicant to highlight publications without there PhD supervisor. However, there are other ways of addressing/prempting such worries. It is therefore not essential to have papers without your PhD supervisor. In fact, for freshly minted PhD I think this would be perfectly normal (although how normal depends on the field).
More generally, it is good to have mixture of different types of publications. Some with, some without your PhD supervisor; some first author, some not; some single author, some in collaborations. How (and if) these are valued differs greatly from field to field, but generally it does not hurt to have the variety.
Let me close by stressing, that all these considerations are secondary to having good, impactful papers. Having your supervisor on your paper can help with both.
(PS. In the comments someone mentioned that in some fields publishing without your supervisor is seen as a cardinal sin. I'm curious about the rational of that.)
Ceteris paribus, a paper in which you are the sole author is preferable to one in which you are merely a co-author. However, you should bear in mind that your supervisor might be able to improve your paper, and so you will need to decide whether you want this assistance. If you are able to publish a scholarly paper without your supervisor's input, and if you judge that the paper would not be improved by taking on your supervisor (or someone else) as a co-author, then that is certainly something that will look good.
