I’m a computer science student who’s taken two discrete math courses where I learned a lot about graph theory and a little bit about combinatorics. I see often that the two fields blend, and I was just wondering why. I see the term “combinatorial graph theory” often as well, and just want to understand better the intertwined relationship between the two.
I bought a graph theory book after my course because I thought the subject was very interesting, and one of the practice problems in the book was what seemed to be a combinatorics question, asking how many chess matches would be played if 5 people played each other only once. I understood that the answer could be found in a complete graph, but is it usually the case where combinatorics questions can be answered with a graph?