29.1. Discrete Mathematics

Try these first

1. 1.

   What is the Ramsey number R(3, 3)?

   Hint

   Think about how connections can form in a group of six.

2. 2.

   Define an articulation point in graph theory.

   Hint

   What happens when you remove a key node?

3. 3.

   What does the Ramsey number R(3, 3) signify?

   • It determines edge count.
   • It indicates friend/enemy groups.
   • It's a type of graph.

   Hint

   Relate it to social interactions.

4. 4.

   True or False? Every tree with n nodes has n edges.

   • True
   • False

   Hint

   Consider basic examples of trees during your answer.

5. 5.

   Create a simple graph with 8 vertices that includes articulation points. What happens when you remove each point?

   Hint

   Use cycles and direct connections creatively.

6. 6.

   Given R(3, 3) is 6, demonstrate for R(4, 4) and conjecture the minimum needed for R(k, k) as k increases.

   Hint

   Sketch graphs to demonstrate increasing complexity.