Strong Lovász conjecture for finite connected vertex-transitive graphs

Let $G$ be a finite connected vertex-transitive graph. A graph is Hamilton connected if it has a Hamilton path between any two vertices, and Hamilton laceable if it is bipartite and has a Hamilton path between any two vertices from different bipartition classes. Strong Lovász conjecture. The graph $G$ is Hamilton connected, Hamilton laceable, a cycle, or one of the five known counterexamples. This strengthens Lovász's conjecture on Hamiltonicity in vertex-transitive graphs and encompasses questions about Hamilton-connected and Hamilton-laceable vertex-transitive graphs. The five exceptional counterexamples are not identified in the supplied text.