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 Dec17 awarded Caucus Dec10 awarded Nice Question Oct22 awarded Popular Question Sep20 awarded Notable Question Sep16 awarded Yearling Jul2 awarded Curious May5 awarded Popular Question Apr1 awarded Popular Question Oct7 asked Relationship between expected and actual value Sep16 awarded Yearling Sep15 awarded Popular Question May23 accepted Proving a simple graph is a connected graph May23 accepted Proofs involving subtrees of a tree May23 accepted Constructing a 3-regular graph with no 3-cycles May23 accepted Counting the number of graphs with a certain property May23 accepted How to show a graph is not Hamiltonian? Apr10 comment Counting the number of graphs with a certain property I found something in the text that says if a graph has an odd cycle, then $\chi (G) \geq 3$. But how do I check all simple graphs with odd cycles to see which follow the property above? Apr10 asked Counting the number of graphs with a certain property Apr3 comment How to show a graph is not Hamiltonian? Thank you very much for the clear answer! I am curious. Does a proof exist that does not require referencing the Petersen graph? (Even if it is the only graph satisfying such requirements) That is, is there some general criteria that would force a graph to be non-Hamiltonian based solely on the number of vertices/girth/regularness? Apr3 comment How to show a graph is not Hamiltonian? $v_G$ is the number of vertices of $G$. I have edited my post to add this explanation!