From my experience with problems in graph theory, these pose certain obstacles that to me seem to particular for discrete mathematics, among them are
1) A solution might be obvious at first sight, but extremely hard to rigorously formulate/proof.
2) A problem statement is very hard to grasp, such that I don't even know how to start.
3) I rarely see a measure of "progress towards a solution"; either I get nowhere or I know from the beginning how to solve a problem/what theorem to use
4) Most problems seem to be "individual" in a sense that I can't identify a general concept that might be helpful for a problem that I will face in the future. In particular that means that finding too strong hints or even full solutions does not help at all. In other fields of math, even copying a well worked out solution might help, since it elucidates in what setting one can properly use a theorem/approach.
Do you have any recommendations of how to figure out conceptual elements in graph theory problem solving, i.e. how to figure out a setting and a general strategy that might be applicable to a certain style of problems?
Are there any good reads in graph theory that point out problem solving strategies/ways of thinking, instead of focusing on results?