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12 votes
1 answer
424 views

Quantitatively characterizing the failure of the converse of Dirac's theorem

First, I am an undergraduate so I apologize if this is trivial and certainly understand if it is closed immediately. I am currently in a combinatorics and graph theory class and recently we have ...
9 votes
1 answer
399 views

Are bipartite Moore graphs Hamiltonian?

This is motivated by a computer-generated conjecture that bipartite distance-regular graphs are hamiltonian. I decided to check the case of Moore graphs first. The cycles and complete bipartite graphs ...
9 votes
2 answers
2k views

"Gray code" of all permutations

Informally asking, can we step through all permutations of the set {1,,n} by just using transpositions? More formally: For any nN let [n]={1,,n} and let Sn be ...