Minimal regular graphs with given girths and crossing numbers
G.L. Chia ; C.S. Gan
Discussiones Mathematicae Graph Theory, Tome 24 (2004), p. 223-237 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:270157 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1227,
     author = {G.L. Chia and C.S. Gan},
     title = {Minimal regular graphs with given girths and crossing numbers},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {24},
     year = {2004},
     pages = {223-237},
     zbl = {1060.05506},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1227}
}

G.L. Chia; C.S. Gan. Minimal regular graphs with given girths and crossing numbers. Discussiones Mathematicae Graph Theory, Tome 24 (2004) pp. 223-237. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1227/

[000] [1] G. Chartrand and L. Lesniak, Graphs & Digraphs (Third edition), (Chapman & Hall, New York 1996).

[001] [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. | Zbl 0271.05105

[002] [3] D.J. Kleitman, The crossing number of K5,n, J. Combin. Theory B 9 (1970) 315-323, doi: 10.1016/S0021-9800(70)80087-4. | Zbl 0205.54401

[003] [4] M. Koman, On nonplanar graphs with minimum number of vertices and a given girth, Commentationes Math. Univ. Carolinae (Prague) 11 (1970) 9-17. | Zbl 0195.25802

[004] [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. | Zbl 0813.05019

[005] [6] M. Nihei, On the girths of regular planar graphs, Pi Mu Epsilon J. 10 (1995) 186-190. | Zbl 0837.05048

[006] [7] B. Richter, Cubic graphs with crossing number two, J. Graph Theory 12 (1988) 363-374, doi: 10.1002/jgt.3190120308. | Zbl 0659.05044

[007] [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. | Zbl 0403.05037

[008] [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.

[009] [10] G.F. Royle, Cubic cages, http://www.cs.uwa.edu.au/~gordon/cages/index.html.

[010] [11] P.K. Wong, Cages - a survey, J. Graph Theory 6 (1982) 1-22, doi: 10.1002/jgt.3190060103. | Zbl 0488.05044