Tutte cycles in circuit graphs

Abstract Jackson and Wormald showed that every 3-connected planar graph G contains a Tutte cycle C such that each component of G - C contains less than | V ( G )|/2 vertices. We prove in this paper that | V ( G )|/2 can be replaced by | V ( G )|/3. This answers a question of Jackson and Wormald. This result may be used to give a better lower bound on the length of a longest cycle in a 3-connected planar graph.

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