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

Discussiones Mathematicae Graph Theory (1999)

- Volume: 19, Issue: 1, page 59-69
- ISSN: 2083-5892

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topMarián Klešč. "The crossing numbers of products of a 5-vertex graph with paths and cycles." Discussiones Mathematicae Graph Theory 19.1 (1999): 59-69. <http://eudml.org/doc/270306>.

@article{MariánKlešč1999,

abstract = {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.},

author = {Marián Klešč},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {graph; drawing; crossing number; path; cycle; Cartesian product; planar drawing},

language = {eng},

number = {1},

pages = {59-69},

title = {The crossing numbers of products of a 5-vertex graph with paths and cycles},

url = {http://eudml.org/doc/270306},

volume = {19},

year = {1999},

}

TY - JOUR

AU - Marián Klešč

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

JO - Discussiones Mathematicae Graph Theory

PY - 1999

VL - 19

IS - 1

SP - 59

EP - 69

AB - 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.

LA - eng

KW - graph; drawing; crossing number; path; cycle; Cartesian product; planar drawing

UR - http://eudml.org/doc/270306

ER -

## References

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- [7] M. Klešč, The crossing numbers of certain Cartesian products, Discuss. Math. Graph Theory 15 (1995) 5-10, doi: 10.7151/dmgt.1001. Zbl0828.05028
- [8] M. Klešč, The crossing number of ${K}_{2,3}\times P\u2099$ and ${K}_{2,3}\times S\u2099$, 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. Zbl0854.05036
- [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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