Some crossing numbers of products of cycles

Marián Klešč

Discussiones Mathematicae Graph Theory (2005)

  • Volume: 25, Issue: 1-2, page 197-210
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Marián Klešč. "Some crossing numbers of products of cycles." Discussiones Mathematicae Graph Theory 25.1-2 (2005): 197-210. <http://eudml.org/doc/270230>.

@article{MariánKlešč2005,
abstract = {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.},
author = {Marián Klešč},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph; drawing; crossing number; cycle; Cartesian product; Cartesian products; cycles},
language = {eng},
number = {1-2},
pages = {197-210},
title = {Some crossing numbers of products of cycles},
url = {http://eudml.org/doc/270230},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Marián Klešč
TI - Some crossing numbers of products of cycles
JO - Discussiones Mathematicae Graph Theory
PY - 2005
VL - 25
IS - 1-2
SP - 197
EP - 210
AB - 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.
LA - eng
KW - graph; drawing; crossing number; cycle; Cartesian product; Cartesian products; cycles
UR - http://eudml.org/doc/270230
ER -

References

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  3. [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. Zbl0403.05037
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  5. [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. Zbl1053.05032
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  9. [9] M. Klešč, On the crossing numbers of Cartesian products of stars and paths or cycles, Mathematica Slovaca 41 (1991) 113-120. Zbl0755.05067
  10. [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. Zbl0949.05018
  11. [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. Zbl0978.05025
  12. [12] M. Klešč, The crossing number of K 2 , 3 × C , Discrete Math. 251 (2002) 109-117. 
  13. [13] M. Klešč and A. Kocúrová, The crossing numbers of products of 5-vertex graphs with cycles, Discrete Math. (to appear). Zbl1118.05021
  14. [14] M. Klešč, R.B. Richter and I. Stobert, The crossing number of C₅×Cₙ, J. Graph Theory 22 (1996) 239-243. Zbl0854.05036
  15. [15] R.B. Richter and G. Salazar, The crossing number of C₆×Cₙ, Australasian J. Combin. 23 (2001) 135-144. Zbl0972.05015
  16. [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. Zbl0820.05015
  17. [17] R.D. Ringeisen and L.W. Beineke, The crossing number of C₃×Cₙ, J. Combin. Theory 24 (B) (1978) 134-136. Zbl0383.05015

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