The following question is similar to another I recently asked, however, it restricts the graph class further by requiring regularity and edge-connectedness to be equal.
Given a $r$-regular, $r$-edge-connected, bipartite graph with $r \ge 2$, will it always contain a Hamiltonian path?
The Horton graph shows that such graphs will not always contain a Hamiltonian cycle (i.e., they may not be Hamiltonian), but is it possible to find a Hamiltonian path in them so that they are still traceable? I tried searching for such a path in the Horton graph with a naive recursive search in Python, but the size of the graph makes it unfeasible.
