Graph Theory (a) Prove that K5 is not planar. Justify all of your work. (b) Prove that G = K2,12 is planar by drawing G without any edge crossings. (c) Give an example of a graph G whose chromatic number is 3, but that contains no K3 as a subgraph. You must prove that your graph actually has chromatic number 3. (d) True or False(circle one):Let G be a simple graph with degree sequence 7,7,7,7,7,7. Then G is planar.
Graph Theory
(a) Prove that K5 is not planar. Justify all of your work.
(b) Prove that G = K2,12 is planar by drawing G without any edge crossings.
(c) Give an example of a graph G whose chromatic number is 3, but that contains no K3 as a subgraph. You must prove that your graph actually has chromatic number 3.
(d) True or False(circle one):Let G be a simple graph with degree sequence 7,7,7,7,7,7. Then G is planar.
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I tried asking this in seperate questions but no body answered . b) Prove that G = K2,12 is planar by drawing G without any edge crossings.
(c) Give an example of a graph G whose chromatic number is 3, but that contains no K3 as a subgraph. You must prove that your graph actually has chromatic number 3.
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