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I'm a beginner at graph theory, and I recently came across the Havel-Hakimi Theorem which is used to determine whether a sequence of integers is graphical. I am using Chartrand and Zhang's Introduction to Graph Theory, but I feel that the proof they provide is lacking. I am wondering whether anyone is aware of a proof for this theorem or where I can find one, preferably an easier one.


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up vote 3 down vote accepted

Pearls in Graph Theory: A Comprehensive Introduction by Hartsfield and Ringel includes a good proof of the theorem. I also believe Google books has the portion of the book about the theorem; It starts around page 10.

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The proof H & R provide is the same one as in my book, but they are much clearer and precise about it. Thank you. – Isaac Kleinman Jun 6 '11 at 15:22

I did a google search, read the first one, and thought it was easy to follow. You can find it here.

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