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Jul 5 at 16:43 comment added Pranay Gorantla I have asked another question about extension to higher dimensions. Here's the link mathoverflow.net/q/474525/149337.
Jul 5 at 7:57 comment added Tony Huynh I haven't checked, but it seems like a similar approach should work in higher dimensions. Feel free to ask it as a separate question.
Jul 4 at 17:20 comment added Pranay Gorantla Just out of curiosity, do you think your proof extends to higher dimensions where I replace interval graphs with box graphs in $\mathbb R^n$? I still assume finite connected graph of maximum degree $\Delta$. I can’t think of how to extend your notion of “contractible” to higher dimensions. If you think I should ask this as a separate question, please let me know and I’ll be happy to.
Jul 4 at 8:49 comment added Tony Huynh You're welcome! I fixed the typos.
Jul 4 at 3:35 history edited Tony Huynh CC BY-SA 4.0
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Jul 4 at 1:29 comment added Pranay Gorantla Thanks a lot! There are some typos: "$z=r_s$ and $z+1=\ell_s$" should be "$z=r_i$ and $z+1=\ell_j$".
Jul 4 at 1:25 vote accept Pranay Gorantla
Jul 3 at 22:32 history edited Tony Huynh CC BY-SA 4.0
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Jul 3 at 22:26 history edited Tony Huynh CC BY-SA 4.0
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Jul 3 at 22:21 history edited Tony Huynh CC BY-SA 4.0
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Jul 3 at 22:07 history answered Tony Huynh CC BY-SA 4.0