Geodesic
Minimal regular graphs with given girths and crossing numbers
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 2, pp. 223-237.

Voir la notice de l'article provenant de la source Library of Science

This paper investigates on those smallest regular graphs with given girths and having small crossing numbers.
Keywords: regular graphs, girth, crossing numbers 
@article{DMGT_2004_24_2_a5,
     author = {Chia, G. and Gan, C.},
     title = {Minimal regular graphs with given girths and crossing numbers},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {223--237},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2004_24_2_a5/}
}
TY  - JOUR
AU  - Chia, G.
AU  - Gan, C.
TI  - Minimal regular graphs with given girths and crossing numbers
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2004
SP  - 223
EP  - 237
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2004_24_2_a5/
LA  - en
ID  - DMGT_2004_24_2_a5
ER  - 
%0 Journal Article
%A Chia, G.
%A Gan, C.
%T Minimal regular graphs with given girths and crossing numbers
%J Discussiones Mathematicae. Graph Theory
%D 2004
%P 223-237
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2004_24_2_a5/
%G en
%F DMGT_2004_24_2_a5
Chia, G.; Gan, C. Minimal regular graphs with given girths and crossing numbers. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 2, pp. 223-237. http://geodesic.mathdoc.fr/item/DMGT_2004_24_2_a5/

[1] G. Chartrand and L. Lesniak, Graphs Digraphs (Third edition), (Chapman Hall, New York 1996).

[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.

[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.

[4] M. Koman, On nonplanar graphs with minimum number of vertices and a given girth, Commentationes Math. Univ. Carolinae (Prague) 11 (1970) 9-17.

[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.

[6] M. Nihei, On the girths of regular planar graphs, Pi Mu Epsilon J. 10 (1995) 186-190.

[7] B. Richter, Cubic graphs with crossing number two, J. Graph Theory 12 (1988) 363-374, doi: 10.1002/jgt.3190120308.

[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.

[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] G.F. Royle, Cubic cages, http://www.cs.uwa.edu.au/~gordon/cages/index.html.

[11] P.K. Wong, Cages - a survey, J. Graph Theory 6 (1982) 1-22, doi: 10.1002/jgt.3190060103.