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Abstrakty
This paper investigates on those smallest regular graphs with given girths and having small crossing numbers.
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Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
223-237
Opis fizyczny
Daty
wydano
2004
Bibliografia
- [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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1227