Finding Tutte paths in linear time

It is well-known that every 2-connected planar graph has a Tutte path, i.e., a path P such that any component of G-P has only two or three attachment points on P. However, it was only recently shown that such Tutte paths can be found in polynomial time. In this paper, we give a new proof that 2-connected planar graphs have Tutte paths which leads easily to a linear-time algorithm to find Tutte paths. Furthermore, for 3-connected planar graphs our Tutte paths come with a system of distinct representatives, a strengthening that allows applications (such as finding 2-walks) to also be done in linear time.

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