Some crossing numbers of products of cycles

• Autorzy: Marián Klešč
• 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

EN

graph; drawing; crossing number; cycle; Cartesian product

Kategorie tematyczne

• 05C10: Planar graphs; geometric and topological aspects of graph theory
• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2005
• Tom: 25
• Numer: 1-2
• Strony: 197-210

Daty

wydano

2005

otrzymano

2003-12-03

poprawiono

2005-02-02

Twórcy

autor

Marián Klešč

• Department of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University, 042 00 Košice, Slovak Republic

Bibliografia

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• [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.
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• [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.

Identyfikatory

DOI

10.7151/dmgt.1272