# On Tutte cycles containing three prescribed edges

@inproceedings{Wigal2021OnTC, title={On Tutte cycles containing three prescribed edges}, author={Michael C. Wigal and Xingxing Yu}, year={2021} }

A cycle C in a graph G is called a Tutte cycle if, after deleting C from G, each component has at most three neighbors on C. Tutte cycles play an important role in the study of Hamiltonicity of planar graphs. Thomas and Yu and independently Sanders proved the existence of Tutte cycles containining three specified edges of a facial cycle in a 2-connected plane graph. We prove a quantitative version of this result, bounding the number of components of the graph obtained by deleting a Tutte cycle…

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