Li et al.'s Tutte-path conjecture for rank-three hypergraph line graphs

A hypergraph is a collection of subsets, called edges, of a ground set; its rank is the maximum edge size. Its line graph has one vertex for each hypergraph edge, with adjacency when two hypergraph edges intersect. A Tutte path is an $(a,b)$-path whose off-path components have at most three neighbours on the path, and a path is maximal if it cannot be extended while preserving the relevant path conditions.

Li et al.'s conjecture. For every pair of vertices $a,b$ of a connected line graph of a hypergraph of rank at most $3$, there is a maximal $(a,b)$-path which is a Tutte path.

The source presents this as an equivalent formulation of Thomassen's open conjecture. It is consequently open, although it is known to be equivalent to the line-graph Hamilton-cycle formulation.