No need to apologize! I haven't heard of the Havel-Hakimi Algorithm before, and I don't have the time to actually try and solve your puzzle right now, but I appreciate the link and will check it out later.
Although just reading the description, I do have one question: What is a "degree sequence"? I going to go ahead and assume that it's https://en.wikipedia.org/wiki/Degree_(graph_theory)#Degree_s.... If that's correct, I'd encourage you to add a hyperlink to the term "degree sequence" with that URL, for people like me with zero background in graph theory.
Although just reading the description, I do have one question: What is a "degree sequence"? I going to go ahead and assume that it's https://en.wikipedia.org/wiki/Degree_(graph_theory)#Degree_s.... If that's correct, I'd encourage you to add a hyperlink to the term "degree sequence" with that URL, for people like me with zero background in graph theory.