As a graduate student, I haven't delved deeply into several discrete math subjects such as combinatorics and graph theory. I have always felt that these areas often present a mishmash of techniques and problems, and I have not been able to construct a cohesive mental framework for appreciate these subjects.
I'm keen to address this deficiency. I am seeking recommendations for resources that encompass various aspects of
- Combinatorics (including extremal and additive types),
- Graph theory (including algebraic approaches),
- Discrete probability, geometry, and related subjects in modern discrete mathematics.
Ideally, I'm searching for the most effective method to grasp these subjects as a graduate student. I want to avoid books that merely skim the surface, spending excessive time on introductory material without delving into relevant techniques. Instead, I'm seeking resources that promptly introduce key techniques and concepts while providing comprehensive coverage of the subject matter. The hope of following this approach is that I can use these topics in my research as well. By following this approach, I hope I can increase my repertoire and perhaps even integrate these topics into my research endeavors as well.
I would greatly appreciate any suggestions you may have.