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2005 | 25 | 1-2 | 197-210
Tytuł artykułu

Some crossing numbers of products of cycles

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The exact values of crossing numbers of the Cartesian products of four special graphs of order five with cycles are given and, in addition, all known crossing numbers of Cartesian products of cycles with connected graphs on five vertices are summarized.
Słowa kluczowe
Wydawca
Rocznik
Tom
25
Numer
1-2
Strony
197-210
Opis fizyczny
Daty
wydano
2005
otrzymano
2003-12-03
poprawiono
2005-02-02
Twórcy
  • Department of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University, 042 00 Košice, Slovak Republic
Bibliografia
  • [1] M. Anderson, R.B. Richter and P. Rodney, The crossing number of C₆×C₆, Congr. Numer. 118 (1996) 97-107.
  • [2] M. Anderson, R.B. Richter and P. Rodney, The crossing number of C₇×C₇, Congr. Numer. 125 (1997) 97-117.
  • [3] L.W. Beineke and R.D. Ringeisen, On the crossing numbers of products of cycles and graphs of order four, J. Graph Theory 4 (1980) 145-155, doi: 10.1002/jgt.3190040203.
  • [4] A.M. Dean and R.B. Richter, The crossing number of C₄×C₄, J. Graph Theory 19 (1995) 125-129, doi: 10.1002/jgt.3190190113.
  • [5] L.Y. Glebsky and G. Salazar, The crossing number of Cₘ×Cₙ is as conjectured for n ≥ m(m+1), J. Graph Theory 47 (2004) 53-72, doi: 10.1002/jgt.20016.
  • [6] F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969).
  • [7] F. Harary, P.C. Kainen and A.J. Schwenk, Toroidal graphs with arbitrarily high crossing numbers, Nanta Math. 6 (1973) 58-67.
  • [8] S. Jendrol' and M. Scerbová, On the crossing numbers of Sₘ×Pₙ and Sₘ×Cₙ, Casopis pro pestování matematiky 107 (1982) 225-230.
  • [9] M. Klešč, On the crossing numbers of Cartesian products of stars and paths or cycles, Mathematica Slovaca 41 (1991) 113-120.
  • [10] M. Klešč, The crossing numbers of products of 5-vertex graphs with paths and cycles, Discuss. Math. Graph Theory 19 (1999) 59-69, doi: 10.7151/dmgt.1085.
  • [11] M. Klešč, The crossing number of (K₄ -e)×C₃, in: Proc. International Scientific Conference on Mathematics (Herl'any, 1999), 106-109, Univ. Technol. Košice, Košice, 2000.
  • [12] M. Klešč, The crossing number of $K_{2,3} × C₃$, Discrete Math. 251 (2002) 109-117.
  • [13] M. Klešč and A. Kocúrová, The crossing numbers of products of 5-vertex graphs with cycles, Discrete Math. (to appear).
  • [14] M. Klešč, R.B. Richter and I. Stobert, The crossing number of C₅×Cₙ, J. Graph Theory 22 (1996) 239-243.
  • [15] R.B. Richter and G. Salazar, The crossing number of C₆×Cₙ, Australasian J. Combin. 23 (2001) 135-144.
  • [16] R.B. Richter and C. Thomassen, Intersections of curve systems and the crossing number of C₅×C₅, Discrete Comput. Geom. 13 (1995) 149-159, doi: 10.1007/BF02574034.
  • [17] R.D. Ringeisen and L.W. Beineke, The crossing number of C₃×Cₙ, J. Combin. Theory 24 (B) (1978) 134-136.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1272
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