Discrete Mathematics with Graph Theory (3rd Edition) 262

Discrete Mathematics with Graph Theory (3rd Edition) 262 -...

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260 4. (b) The graph corresponding to the cubes is drawn to the right. It is not possible to find two edge disjoint subgraphs, so there is no solution. Solutions to Review Exercises (c) Here are the graph corresponding to the' cubes and two edge disjoint subgraphs. 2~ R B R 3D, ~ 4 (jJ G W G 1 F B R L Cube 4 R G W R Here is the solution indicated. Cube 3 G R B G Cube 2 B B R W Cube 1 W W G B (d) We present below the graph which corresponds to the cubes and two edge disjoint subgraphs.
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Unformatted text preview: 4 4 F B R L Cube 4 B R W G Here is the solution indicated. Cube 3 R W G B Cube 2 G B R W Cube 1 W G B R (a) N;1 (b) Dl!1 (c) It is not possible. For the conditions in 4(a) and 4(b) to be hold simultaneously,the graph would have to have exactly three odd vertices. This is impossible by Corollary 9.2.6....
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