Minimal regular graphs with given girths and crossing numbers

G.L. Chia; C.S. Gan

Discussiones Mathematicae Graph Theory (2004)

  • Volume: 24, Issue: 2, page 223-237
  • ISSN: 2083-5892

Abstract

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This paper investigates on those smallest regular graphs with given girths and having small crossing numbers.

How to cite

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G.L. Chia, and C.S. Gan. "Minimal regular graphs with given girths and crossing numbers." Discussiones Mathematicae Graph Theory 24.2 (2004): 223-237. <http://eudml.org/doc/270157>.

@article{G2004,
abstract = {This paper investigates on those smallest regular graphs with given girths and having small crossing numbers.},
author = {G.L. Chia, C.S. Gan},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {regular graphs; girth; crossing numbers},
language = {eng},
number = {2},
pages = {223-237},
title = {Minimal regular graphs with given girths and crossing numbers},
url = {http://eudml.org/doc/270157},
volume = {24},
year = {2004},
}

TY - JOUR
AU - G.L. Chia
AU - C.S. Gan
TI - Minimal regular graphs with given girths and crossing numbers
JO - Discussiones Mathematicae Graph Theory
PY - 2004
VL - 24
IS - 2
SP - 223
EP - 237
AB - This paper investigates on those smallest regular graphs with given girths and having small crossing numbers.
LA - eng
KW - regular graphs; girth; crossing numbers
UR - http://eudml.org/doc/270157
ER -

References

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  1. [1] G. Chartrand and L. Lesniak, Graphs & Digraphs (Third edition), (Chapman & Hall, New York 1996). 
  2. [2] R.K. Guy and A. Hill, The crossing number of the complement of a circuit, Discrete Math. 5 (1973) 335-344, doi: 10.1016/0012-365X(73)90127-1. Zbl0271.05105
  3. [3] D.J. Kleitman, The crossing number of K 5 , n , J. Combin. Theory B 9 (1970) 315-323, doi: 10.1016/S0021-9800(70)80087-4. Zbl0205.54401
  4. [4] M. Koman, On nonplanar graphs with minimum number of vertices and a given girth, Commentationes Math. Univ. Carolinae (Prague) 11 (1970) 9-17. Zbl0195.25802
  5. [5] D. McQuillan and R.B. Richter, On 3-regular graphs having crossing number at least 2, J. Graph Theory, 18 (1994) 831-839, doi: 10.1002/jgt.3190180807. Zbl0813.05019
  6. [6] M. Nihei, On the girths of regular planar graphs, Pi Mu Epsilon J. 10 (1995) 186-190. Zbl0837.05048
  7. [7] B. Richter, Cubic graphs with crossing number two, J. Graph Theory 12 (1988) 363-374, doi: 10.1002/jgt.3190120308. Zbl0659.05044
  8. [8] R.D. Ringeisen and L.W. Beineke, 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. Zbl0403.05037
  9. [9] G.F. Royle, Graphs and multigraphs, in: C.J. Colbourn and J.H. Dinitz ed., The CRC Handbook of Combinatorial Designs, (CRC Press, New York, 1995) 644-653. 
  10. [10] G.F. Royle, Cubic cages, http://www.cs.uwa.edu.au/~gordon/cages/index.html. 
  11. [11] P.K. Wong, Cages - a survey, J. Graph Theory 6 (1982) 1-22, doi: 10.1002/jgt.3190060103. Zbl0488.05044

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