What is the difference between graph theory and combinatorics?

What is the difference between graph theory and combinatorics?

Graph theory focuses on the study of graphs, which are mathematical structures used to model pairwise relations between objects. Combinatorics, on the other hand, deals with counting, arrangement, and combination of objects.

Can you give me an example of a problem in graph theory?

Sure! A classic problem in graph theory is the 'Seven Bridges of Königsberg,' where the challenge is to find a walk through the city that crosses each bridge exactly once.

What about combinatorics? Any interesting problems?

Absolutely! One famous combinatorial problem is the 'Birthday Paradox,' which explores the probability that in a group of people, at least two will share the same birthday.

How are these two fields related?

They are closely related! Many problems in combinatorics can be represented using graphs, and techniques from one field can often be applied to the other.