On 3-Connected Plane Graphs without Triangular Faces
نویسندگان
چکیده
We prove that each polyhedral triangular face free map G on a compact 2-dimensional manifold M with Euler characteristic (M) contains a k-path, i.e. a path on k vertices, such that each vertex of this path has, in G, degree at most 5 2 k if M is a sphere S 0 and at most k 2 5+ p 49?24(M 2 if M 6 = S 0 or does not contain any k-path. We show that for even k this bound is best possible. Moreover, we verify that for any graph other than a path no similar estimation exists.
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 77 شماره
صفحات -
تاریخ انتشار 1999