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Light paths with an odd number of vertices in large polyhedral maps (1998)

Jendrol', S. ; Voss, H. -J.

Springer

Annals of combinatorics 2 (1998), S. 313-324

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ISSN: 0219-3094

Keywords: 05C10 ; 05C38 ; 52B10 ; path ; polyhedral map ; embeddings

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract LetP k be a path onk vertices. In this paper we prove that (1) every polyhedral map on the torus and the Klein bottle contains a pathP k such that each of its vertices has degree ≤6k−2 ifk is odd,k≥3, (2) every large polyhedral map on any compact 2-manifoldM with Euler characteristic χ(M)〈0 contains a pathP k such that each of its vertices has degree ≤ 6k − 2 ifk is odd,k≥3, (3) moreover, these bounds are attained. Fork=1 ork even,k≥2, the bound is 6k which has been proved in our previous paper.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01608528

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