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Feb 27, 2023 at 16:03 comment added HenrikRüping The linked proof of the correctness of the Havel-Hakimi algorithm also seems to imply that any two realizations can be obtained from each other by a sequence of replacements of the following form: Pick 4 vertices $A,B,C,D$ so that there are edges $AB$ and $CD$, but no edges $AC$ and $BD$. Then replace the edges $AB$ and $CD$ by $AC$ and $BD$.
Feb 27, 2023 at 14:38 vote accept Jeremiah
Feb 27, 2023 at 13:54 history edited Max Alekseyev CC BY-SA 4.0
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Feb 27, 2023 at 13:49 history answered Max Alekseyev CC BY-SA 4.0