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1999 | 19 | 1 | 59-69

Tytuł artykułu

The crossing numbers of products of a 5-vertex graph with paths and cycles

Autorzy

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
There are several known exact results on the crossing numbers of Cartesian products of paths, cycles or stars with "small" graphs. Let H be the 5-vertex graph defined from K₅ by removing three edges incident with a common vertex. In this paper, we extend the earlier results to the Cartesian products of H × Pₙ and H × Cₙ, showing that in the general case the corresponding crossing numbers are 3n-1, and 3n for even n or 3n+1 if n is odd.

Słowa kluczowe

Wydawca

Rocznik

Tom

19

Numer

1

Strony

59-69

Daty

wydano
1999
otrzymano
1998-06-09
poprawiono
1998-11-21

Twórcy

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

Bibliografia

  • [1] D. Archdeacon, R.B. Richter, On the parity of crossing numbers, J. Graph Theory 12 (1988) 307-310, doi: 10.1002/jgt.3190120302.
  • [2] L.W. Beineke, 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.
  • [3] F. Harary, Graph Theory (Addison - Wesley, Reading, MA, 1969).
  • [4] S. Jendrol', M. S cerbová, On the crossing numbers of Sₘ × Pₙ and Sₘ × Cₙ, Casopis pro pestování matematiky 107 (1982) 225-230.
  • [5] M. Klešč, On the crossing numbers of Cartesian products of stars and paths or cycles, Mathematica Slovaca 41 (1991) 113-120.
  • [6] M. Klešč, The crossing numbers of products of paths and stars with 4-vertex graphs, J. Graph Theory 18 (1994) 605-614.
  • [7] M. Klešč, The crossing numbers of certain Cartesian products, Discuss. Math. Graph Theory 15 (1995) 5-10, doi: 10.7151/dmgt.1001.
  • [8] M. Klešč, The crossing number of $K_{2,3} × Pₙ$ and $K_{2,3} × Sₙ$, Tatra Mountains Math. Publ. 9 (1996) 51-56.
  • [9] M. Klešč, R.B. Richter, I. Stobert, The crossing number of C₅ × Cₙ, J. Graph Theory 22 (1996) 239-243.
  • [10] A.T. White, L.W. Beineke, Topological graph theory, in: Selected Topics in Graph Theory (Academic Press, London, 1978) 15-49.

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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1085