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(a) Let G = (V,E) be a loop-free connected graph with |V| ≥ 11. Prove that either G or its complement G must be nonplanar. (b) The result in part (a) is actually true for |V| ≥ 9, but the proof for |V| harder. Find a counterexample to part (a) for |V| = 8. = 9, 10 is much

(a) Let G = (V,E) be a loop-free connected graph with |V| ≥ 11. Prove that either G or its complement G must be nonplanar. (b) The result in part (a) is actually true for |V| ≥ 9, but the proof for |V| harder. Find a counterexample to part (a) for |V| = 8. = 9, 10 is much

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. Answer these two questions:

 

(a) Let G = (V,E) be a loop-free connected graph with |V| ≥ 11. Prove that either G or its complement G must be nonplanar. (b) The result in part (a) is actually true for |V| ≥ 9, but the proof for |V| harder. Find a counterexample to part (a) for |V| = 8. = 9, 10 is much
Transcribed Image Text:(a) Let G = (V,E) be a loop-free connected graph with |V| ≥ 11. Prove that either G or its complement G must be nonplanar. (b) The result in part (a) is actually true for |V| ≥ 9, but the proof for |V| harder. Find a counterexample to part (a) for |V| = 8. = 9, 10 is much
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