TITLE: Are bipartite Moore graphs Hamiltonian?
QUESTION [9 upvotes]: 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 are hamiltonian (trivial).
The girth-6 graphs are the incidence graphs of the projective planes. The classical finite-field planes are hamiltonian by
Singer, but there are lots of nonclassical planes.
And what about the girth-8 and girth-12 case?
EDIT: Corrected the girth-6 case as pointed out by Gordon Royle.

REPLY [2 votes]: This recent paper of Sato and Suzuki shows that the graphs corresponding to some classical generalized quadrangles are indeed Hamiltonian: 
Sato, H. & Suzuki, H. Graphs and Combinatorics (2018). https://link.springer.com/article/10.1007/s00373-018-1940-6