Local structures in polyhedral maps on surfaces, and path transferability of graphs

Details Local structures in polyhedral maps on surfaces, and path transferability of graphs Local structures in polyhedral maps on surfaces, and path transferability of graphs

2009-04-26

arxiv.org/abs/0904.4012v1

Mathematics

Combinatorics

1 table, and 3 figures

Scientific paper

We extend Jendrol' and Skupie\'n's results about the local structure of maps on the 2-sphere: In this paper we show that if a polyhedral map $G$ on a surface $\M$ of Euler characteristic $\chi (\M) \le 0$ has more than $126|\chi (\M)|$ vertices, then $G$ has a vertex with "nearly" non-negative combinatorial curvature. As a corollary of this, we can deduce that path transferability of such graphs are at most 12.

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