Final answer:
The difficulty of topics in graph theory can range widely, with advanced areas like computational complexity and the P versus NP problem being particularly formidable. Graph coloring problems offer a useful example of how graph theory challenges can vary from basic to highly complex.
Step-by-step explanation:
When discussing the topic in graph theory that is considered the most difficult, it varies greatly depending on the complexity of the problems and the level of the student.
However, some of the more challenging areas in graph theory could involve advanced topics like computational complexity theory, especially problems related to NP-complete problems, the P versus NP problem, and randomized algorithms.
Graph theory encompasses a wide range of difficulties, from introductory concepts that are accessible to high school students, to cutting-edge research problems that challenge even professional mathematicians.
In the context of the provided information, identifying categories with the most blue squares or red squares might relate to graph coloring problems, which can range from simple to extremely hard based on the constraints and size of the graph.