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The crossing number of Cm × Cn is as conjectured for n ≥ m(m + 1)

✍ Scribed by Lev Yu. Glebsky; Gelasio Salazar

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
168 KB
Volume
47
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

It has been long conjectured that the crossing number of C~m~ × C~n~ is (m−2)n, for all m, n such that n ≥  m ≥  3. In this paper, it is shown that if n ≥  m(m + 1) and m ≥  3, then this conjecture holds. That is, the crossing number of C~m~ × C~n~ is as conjectured for all but finitely many n, for each m. The proof is largely based on techniques from the theory of arrangements, introduced by Adamsson and further developed by Adamsson and Richter. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 53–72, 2004

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