Tutte trails of graphs on surfaces
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A Tutte trail T of a graph G is a trail such that every component of GnV (T) has at most three edges connecting it to T. In 1992, Bill Jackson conjectured that every 2-edge-connected graph G has a Tutte closed trail. In this thesis, we show that Jackson's conjecture is true when G is embedded on the plane and the projective plane. We also give some partial results when G is embedded on the torus.
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