I'm currently a PhD student in theoretical computer science. I've been working on this problem daily for almost a month that has been well studied and was assigned to me by my advisor. The problem is specifically about establishing an upper bound on coloring a special class of graphs with some interesting properties. However, the last major improvement on the upper bound dates almost 20 years ago in SODA.
As I am sure some of you are aware, establishing upper bounds on coloring involves "playing" around with different coloring constructions and trying to establish an upper bound for that construction. However, so far, all my constructions (that I achieved without reading any literature on the problem) have lead to ever so slightly worse bounds to the existing literature (I know the best current bound).
My question is, when is a good time to give up and start reading other people's work? I have tens of ideas on different coloring arguments that I want to explore, but I am not sure if I am stuck in "naive" land using tools that will get me nowhere. Should I just call it quits and start reading what other people have done? My advisor told me he would be supportive in both decisions (which I am very thankful for), but that ultimately the decision is mine (although he prefers me starting to read). Any advice?