My Math Forum Graph theory: Prove that each cycle has minimum length of 5

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 December 13th, 2015, 05:37 AM #1 Newbie   Joined: Dec 2015 From: Germany Posts: 1 Thanks: 0 Graph theory: Prove that each cycle has minimum length of 5 How do I prove that each cycle in this graph has a minimum length of 5?
 December 29th, 2015, 11:58 AM #2 Member   Joined: Jun 2009 Posts: 83 Thanks: 1 Hi, I think it suffices to prove it for selected fixed vertex v0 - because the graph is symmetric (automorphism is eg. every mapping sending vertex v to vertex not adjacent with v). And checking it for v0 is easy - it can be seen that cycle of length 3 and 4 doesn't exist.
 March 22nd, 2016, 09:33 AM #3 Newbie   Joined: Mar 2016 From: Slovenia Posts: 1 Thanks: 0 How do I prove that every circulant of girth at least 4 and with degree 4 is non-planar?

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