Arrangements, circular arrangements and the crossing number of C7 x Cn

被引：25
|
作者：
Adamsson, J
Richter, RB [1 ]
机构：
[1] Univ Prince Edward Isl, Dept Math & Stat, Charlottetown, PE C1A 4P3, Canada
[2] Univ Waterloo, Dept Combinator & Optimizat, Waterloo, ON N2L 3G1, Canada
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES B | 2004年 / 90卷 / 01期
关键词：
D O I：
10.1016/j.jctb.2003.05.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Motivated by the problem of determining the crossing number of the Cartesian product C-m x C-n of two cycles, we introduce the notion of an (m,n)-arrangement, which is a generalization of a planar drawing of Pn+1 x C-m in which the two "end cycles" are in the same face of the remaining n cycles. The main result is that every (m, n)-arrangement has at least (m - 2)n crossings. This is used to show that the crossing number of C-7 x C-n is 5n, in agreement with the general conjecture that the crossing number of C-m x C-n is (m - 2)n, for 3 less than or equal to m less than or equal to n. (C) 2003 Elsevier Inc. All rights reserved.
引用
收藏
页码：21 / 39
页数：19
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