THEOREM 4.11
Let G be a simple graph with n (≥ 3) vertices and m edges. Then the thickness t (G) of G satisfies the inequalities
t(G) ≥ ⌈m/(3n − 6)⌉ and t(G) ≥ ⌊(m + 3n − 7)/(3n − 6)⌋.
Use Theorem 4.11 on this page to help with the requirements.
– Select and discuss a graph, G, with thickness 2
— Show the graph and provide ALL of the descriptive information, e.g. vertex set, edge set, degree sequence, …
— 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, e.g. vertex set, edge set, degree sequence, …
— 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, e.g. vertex set, edge set, degree sequence, …
— 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
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