I'm familiar with the article on whether song titles are able to copyrighted or trademarked. You should note that there are no absolute conclusions reached with the exception of some extreme examples.
Disclaimer: I actually owned the "Yellow Submarine" book when I was younger and it was one of my favorite possessions.
Let's begin by discussing what type of intellectual property we're talking about. Trademark means a brand, e.g. source of origin - an identifier for products and services. If you were selling books under the guise of "Yellow Submarine" publishing company, you've raised a trademark issue. But if you've titled your book "Yellow Submarine" which sums up your dreams about wanting to be a submariner, that's actually a work of authorship and copyright question, not a trademark question. However, there can be implications regarding trademark rights and usage as sometimes these unique titles can be trademarked too.
The article discusses the type of words and the usage and what is the thinking behind intellectual property protection. "On the road again" is a more generic phrase. Removing those words from language is problematic and not within the spirit of the type of original works that the law intends to protect. How could we reserve those words for one party? Now if you using the title of a song for another song that is highly unusual, unique and not generally within common communication - "Sergeant Pepper's Lonely Hearts Club Band" - then issues may arise. The courts will decide the boundaries. The title "Yellow Submarine" in the above context may be a challenging case to prosecute.
As to international copyright and trademark laws, those are usually subject to a treatise. If your intention is to enter the United States using Yellow Submarine in some fashion, then be aware of what barriers you may have for use.