29.1.2. Question 1

Try these first

1. 1.

   What is the complement of a graph?

   Hint

   Think about what happens to the edges.

2. 2.

   Define a simple graph.

   Hint

   It’s about the format of the edges.

3. 3.

   What is a graph's complement?

   • True
   • False

   Hint

   Think about edges that 'should' be there.

4. 4.

   Ramsey numbers guarantee mutual relationships in groups. Is this true?

   • True
   • False

   Hint

   Remember the group sizes.

5. 5.

   Given a simple graph with 6 nodes, prove that it must contain at least one complete subgraph K3 or its complement K3.

   Hint

   Refer back to our discussions about structure in social settings.

6. 6.

   Consider a scenario with more than 6 nodes. Discuss how Ramsey numbers predict relationship dynamics.

   Hint

   How do the numbers scale as groups get larger?