Mathematical analysis demonstrates an equivalent formulation of Thomassen's conjecture in claw-free graphs, indicating a new pathway to resolve Hamilton cycle conjectures.
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.
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Adam Kabela (2026) studied this question.
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