Embedding grids in surfaces
نویسندگان
چکیده
We show that if a very large grid is embedded in a surface, then a large subgrid is embedded in a disc in the surface. This readily implies that: (a) a minor-minimal graph that does not embed in a given surface has no very large grid; and (b) a minor-minimal k-representative embedding in the surface has no very large grid. Similar arguments show (c) that if G is minimal with respect to crossing number, then G has no very large grid. This work is a refinement of Thomassen (J. Combin. Theory Ser. B 70 (1997) 306). © 2004 Elsevier Ltd. All rights reserved.
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عنوان ژورنال:
- Eur. J. Comb.
دوره 25 شماره
صفحات -
تاریخ انتشار 2004