A proof of the crossing number of K 3 , n in a surface

Pak Tung Ho

Discussiones Mathematicae Graph Theory (2007)

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

Abstract

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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)⎦).

How to cite

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Pak 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

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  1. [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. [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. [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. [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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