Embedding grids in surfaces

被引：21
作者：
Geelen, JF [1 ]
Richter, RB
Salazar, G
机构：
[1] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada
[2] Univ Autonoma San Luis Potosi, Inst Invest Comun Opt, San Luis Potosi 78210, Mexico
来源：
EUROPEAN JOURNAL OF COMBINATORICS | 2004年 / 25卷 / 06期
基金：
加拿大自然科学与工程研究理事会;
关键词：
D O I：
10.1016/j.ejc.2003.07.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 OF 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). (C) 2004 Elsevier Ltd. All rights reserved.
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页码：785 / 792
页数：8
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