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Mar 25, 2018 at 8:36 answer added landon rabern timeline score: 4
Oct 18, 2017 at 20:41 comment added Abdelmalek Abdesselam Beautiful answer by Fedor and elaboration by you. In case this may help for your general line of inquiry, you can find an example with 15 vertices for the triple $(10,8,7)$ in sciencedirect.com/science/article/pii/S0021869315005657
Oct 18, 2017 at 20:27 answer added Peter Heinig timeline score: 16
Oct 18, 2017 at 16:14 vote accept Peter Heinig
Oct 18, 2017 at 12:01 answer added Fedor Petrov timeline score: 40
Oct 18, 2017 at 10:25 history edited Peter Heinig CC BY-SA 3.0
Added remark that random regular graphs also don't yield an example.
Oct 18, 2017 at 10:04 history asked Peter Heinig CC BY-SA 3.0