The crossing number of  C m   ×  C n   is as conjectured for  n  ≥  m ( m  + 1) | Zendy

Glebsky Lev Yu. | Zendy; Salazar Gelasio | Zendy

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

Author(s) -

Glebsky Lev Yu.,

Salazar Gelasio

Publication year - 2004

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.20016

Subject(s) - mathematics , conjecture , combinatorics , crossing number (knot theory) , graph , discrete mathematics , intersection (aeronautics) , engineering , aerospace engineering

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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