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May 27, 2014 at 17:19 comment added Felix Goldberg @KetilTveiten Sorry, my mistake. $K_{2,3}$ is also non-obvious. Thanks!
May 27, 2014 at 14:36 comment added Ketil Tveiten Forgive me if I am being dim, but how do you add an edge to $K_{2,3}$ to get a regular graph? You have three vertices with degree 2...
May 27, 2014 at 14:33 comment added joro I didn't address adding edges, just deleting edges. Thought you claimed both your constructions work.
May 27, 2014 at 14:31 comment added Felix Goldberg $K_{2,3}$ is obvious because you can add an edge to obtain a $3$-regular graph. However, for $n >2$ this does seem to be a family of counter-examples. Are there others?
May 27, 2014 at 14:22 history answered joro CC BY-SA 3.0