Equivalent Formulation of Thomassen's Conjecture Using Tutte Paths in Claw‐Free Graphs

ABSTRACT We continue studying Thomassen's conjecture (every 4‐connected line graph has a Hamilton cycle) in the direction of a recently shown equivalence with Jackson's conjecture (every 2‐connected claw‐free graph has a Tutte cycle), and we extend the equivalent formulation as follows: In every connected claw‐free graph, any two vertices are connected by a maximal path which is a Tutte path.