Abstract
For a positive integer k ≥ 4 , a graph G is called k - ordered, if for any ordered set of k distinct vertices of G , G has a cycle that contains all the vertices in the designated order. Goddard (2002) [3] showed that every 4-connected triangulation of the plane is 4-ordered. In this paper, we improve this result; every 4-connected triangulation of any surface is 4-ordered. Our proof is much shorter than the proof by Goddard.
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