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Timeline for $(k,n)$-binary graphs

Current License: CC BY-SA 4.0

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Oct 3, 2018 at 0:01 vote accept Dominic van der Zypen
Oct 2, 2018 at 16:21 comment added Gerhard Paseman No biggie. You might observe that F and G have Hamiltonian cycles (sort of) which I think lead to a quick proof of longest path, or at least a good lower bound. Gerhard "Prefers Easy Arguments This Morning" Paseman, 2018.10.02.
Oct 2, 2018 at 16:14 comment added Philipp Lampe @GerhardPaseman Sorry, when writing the answer I had not really noticed your second comment that an easy parity argument works for all even $k$. So I have made the answer CW and added the remark about even $k$.
Oct 2, 2018 at 16:09 history edited Philipp Lampe CC BY-SA 4.0
Added discussion for general $k$; made community wiki. ; Post Made Community Wiki
Oct 2, 2018 at 16:06 comment added Gerhard Paseman Never mind. Let F be the subset with an even number of zeros and G a component with an odd number of zeros. F and G are connected components, and F is connected to G iff k is odd. I think the longest path can be found by an appropriate traversal of F and G. Gerhard "Coffee Not Working Fast Today" Paseman, 2018.10.02.
Oct 2, 2018 at 16:00 comment added Gerhard Paseman Can you confirm my conjecture above about even k? Gerhard "Almost Sure It Is Obvious" Paseman, 2018.10.02.
Oct 2, 2018 at 15:57 history answered Philipp Lampe CC BY-SA 4.0