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Theorem 2 (Kuratowski) says that a graph is nonplanar if and only if it contains a subgraph homeomorphic to <math> K_{3,3} </math> or <math> K_{5} </math>.<br> | Theorem 2 (Kuratowski) says that a graph is nonplanar if and only if it contains a subgraph homeomorphic to <math> K_{3,3} </math> or <math> K_{5} </math>.<br> | ||
| − | Looking at the given graph, it is obvious to see that it contains a subgraph homeomorphic to <math> K_{5} </math>. Therefore, the given graph is nonplanar.<br><br> | + | Looking at the given graph, it is obvious to see that it contains a subgraph homeomorphic to <math> K_{5} </math> (a, c, d, f, and h form the pentagon, and everything inside of the pentagon forms the rest of <math> K_{5}</math>. Therefore, the given graph is nonplanar.<br><br> |
--[[User:Aoser|Aoser]] 16:59, 5 December 2008 (UTC) | --[[User:Aoser|Aoser]] 16:59, 5 December 2008 (UTC) | ||
Latest revision as of 12:02, 5 December 2008
Theorem 2 (Kuratowski) says that a graph is nonplanar if and only if it contains a subgraph homeomorphic to $ K_{3,3} $ or $ K_{5} $.
Looking at the given graph, it is obvious to see that it contains a subgraph homeomorphic to $ K_{5} $ (a, c, d, f, and h form the pentagon, and everything inside of the pentagon forms the rest of $ K_{5} $. Therefore, the given graph is nonplanar.
--Aoser 16:59, 5 December 2008 (UTC)
