This project looks at the thickness of nonplanar graphs. Thickness is a difficult topic due to the lack of theoretical results. However, an investigation into the thickness of nonplanar graphs offers excellent insight into planar graphs. Below are the specific requirements for Project 2.
Use Theorem 4.11 on page 90 to help with the requirements.
– Select and discuss a graph, G, with thickness 2
— Show the graph and provide all of the descriptive information
— Show the planar graphs that can be superimposed to form G
– Select and discuss a graph, H, with thickness 3
— Show the graph and provide all of the descriptive information
— Show the planar graphs that can be superimposed to form H
– Select and discuss a maximal planar graph with 8 vertices
— Show the graph and provide all of the descriptive information
— Discuss how the addition of a single edge creates a graph of thickness 2
— Show the planar graphs that can be superimposed to form the graph with its additional edge
– Discuss some generalizations about graphs of thickness 2
— Let us know what you learned during this project
— Provide additional graphs as required
A few notes about format: use MS PowerPoint for your presentation; develop a presentation that is 10-20 slides in length; incorporate audio files into your presentation in order to explain your work; use Equation Editor for all mathematical symbols, e.g. x ∈ X or Cl(A) ⋂ Cl(X-A); and select fonts, backgrounds, etc. to make your presentation look professional.