Discrete Mathematics with Graph Theory (3rd Edition) 376

# Discrete Mathematics with Graph Theory (3rd Edition) 376 -...

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374 6~lCd 2 ~ 'f 5 3 4 Solutions to Exercises Note that other relationships are sat- isfied here, although they weren't re- quired. There is, however, no way to get 2 and III adjacent. a ~ . b h c 9 d f e 1i is not 2-colorable because there are circuits of odd length. Removing one vertex will not be good enough. (Removing one edge from K6 does not make it planar.) Since removing two still does not make it planar (there will always be a subgraph isomorphic to K5 or
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Unformatted text preview: K3,3), we discover that three vertices must be removed from 1i. You have to be careful which three. We remove b, c and 9 as shown. Here are (J' and a floor plan. ~ ~ 4 12. (a) (Jl 1i is 2-colorable. Here are (J' and a possible floor plan. 1 @ II 2 b 4 IV ill 3 ffl4 O!{J. 2 '1 Here plan. !f}. 11 are (J' and a possible floor IV III Note that X(1i) = 2, as shown, so no vertex needs to be removed. I 4 I 1 III I IV 3 I 2 III...
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## This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.

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