Jackson–Yoshimoto's spanning even tree conjecture for regular nonbipartite graphs

Let $G$ be a finite connected graph, possibly with multiple edges but no loops. A spanning tree $T$ of $G$ is even if all leaves of $T$ belong to the same part of the bipartition of $T$. Jackson–Yoshimoto's conjecture. Every regular nonbipartite connected graph has a spanning even tree.

The conjecture asserts the existence of such a tree without the additional 2-factor hypothesis in the partial result preceding it. It is resolved by the paper's result that every connected graph that is not a regular bipartite graph has a spanning weakly even tree; in particular, every regular nonbipartite connected graph has a spanning even tree.