# A proof of the crossing number of ${K}_{3,n}$ in a surface

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 3, page 549-551
- ISSN: 2083-5892

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topPak Tung Ho. "A proof of the crossing number of $K_{3,n}$ in a surface." Discussiones Mathematicae Graph Theory 27.3 (2007): 549-551. <http://eudml.org/doc/270141>.

@article{PakTungHo2007,

abstract = {In this note we give a simple proof of a result of Richter and Siran by basic counting method, which says that the crossing number of $K_\{3,n\}$ in a surface with Euler genus ε is
⎣n/(2ε+2)⎦ n - (ε+1)(1+⎣n/(2ε+2)⎦).},

author = {Pak Tung Ho},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {crossing number; bipartite graph; surface},

language = {eng},

number = {3},

pages = {549-551},

title = {A proof of the crossing number of $K_\{3,n\}$ in a surface},

url = {http://eudml.org/doc/270141},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Pak Tung Ho

TI - A proof of the crossing number of $K_{3,n}$ in a surface

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 3

SP - 549

EP - 551

AB - In this note we give a simple proof of a result of Richter and Siran by basic counting method, which says that the crossing number of $K_{3,n}$ in a surface with Euler genus ε is
⎣n/(2ε+2)⎦ n - (ε+1)(1+⎣n/(2ε+2)⎦).

LA - eng

KW - crossing number; bipartite graph; surface

UR - http://eudml.org/doc/270141

ER -

## References

top- [1] R.K. Guy and T.A. Jenkyns, The toroidal crossing number of ${K}_{m,n}$, J. Combin. Theory 6 (1969) 235-250, doi: 10.1016/S0021-9800(69)80084-0. Zbl0176.22303
- [2] R.B. Richter and J. Siran, The crossing number of ${K}_{3,n}$ in a surface, J. Graph Theory 21 (1996) 51-54, doi: 10.1002/(SICI)1097-0118(199601)21:1<51::AID-JGT7>3.0.CO;2-L Zbl0838.05033
- [3] G. Ringel, Das Geschlecht des vollständigen paaren Graphen, Abh. Math. Sem. Univ. Hamburg 28 (1965) 139-150, doi: 10.1007/BF02993245. Zbl0132.21203
- [4] G. Ringel, Der vollständige paare Graph auf nichtorientierbaren Flächen, J. Reine Angew. Math. 220 (1965) 88-93, doi: 10.1515/crll.1965.220.88. Zbl0132.21204

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