Unformatted text preview: C 3 and P 4 below: C 3 P 4 P 4 ± C 3 (a) (5 points) Prove that χ ( G ± H ) ≤ χ ( G ) χ ( H ). (b) (5 points) Prove that χ ( G ) + χ ( H )2 ≤ χ ( G ± H ) ≤ χ ( G ) + χ ( H ) + 1. 5. (10 points) The cube Q 4 consists of sixteen vertices associated with the sixteen bitstrings 0000 , 0001 ,..., 1111. Two vertices are adjacent if they diﬀer in exactly one bit. Prove that Q 4 is nonplanar. 6. (10 points) Prove by construction that for n > 2 k , ex( C 2 k ,n ) ≥ 2 k ( n2 k ). Page 1 of 1 April 8, 2010...
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 Spring '09
 WILDSTROM
 Math, Graph Theory, Trigraph, Ordered pair, Leonhard Euler

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