Tutte cycles in circuit graphs Original Research Article

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.