nach oben

Designs, Codes and Cryptography

Erschienen in:

01.05.2015

4-Cycle decompositions of \(( \lambda +m)K_{v+u} {\setminus } \lambda K_v\)

verfasst von: N. A. Newman

Erschienen in: Designs, Codes and Cryptography | Ausgabe 2/2015

Einloggen, um Zugang zu erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper we solve the problem of decomposing \(( \lambda +m)K_{v+u} {\setminus } \lambda K_v\) into 4-cycles for all \(m>0\) and \(u \ge 1\). This paper extends the results of “Enclosings of \(\lambda \)-fold 4-cycle systems” [Newman and Rodger, Des. Codes Cryptogr. 55:297–310 (2010)].

Vorheriger Artikel A new family of relative hemisystems on the Hermitian surface

Nächster Artikel A construction of a partial difference set in the extraspecial groups of order with exponent

Andersen L.D., Hilton A.J.W., Mendelsohn E.: Embedding partial Steiner triple systems. Proc. Lond. Math. Soc. 41, 557–576 (1980).

Bermond J.-C., Huang C., Sotteau D.: Balanced cycle and circuit designs: even cases. Ars Comb. 5, 292–318 (1978).

Billington E.J., Fu H., Rodger C.A.: Packing complete multipartite graphs with 4-cycles. J. Comb. Des. 9, 107–127 (2001).

Bryant D.E., Rodger C.A.: The Doyen–Wilson theorem extended to \(5\)-cycle. J. Comb. Theory 68, 218–225 (1994).

Bryant D.E., Rodger C.A.: On the Doyen–Wilson theorem for \(m\)-cycle systems. J. Comb. Des. 4, 253–271 (1994).

Bryant D.E., Rodger C.A., Spicer E.R.: Embeddings of \(m\)-cycle systems and incomplete \(m\)-cycle systems: \(m \le 14\). Discret. Math. 171, 55–75 (1997).

Bryant D., Horsley D., Maenhaut B.: Decompositions into 2-regular subgraphs and equitable partial cycle decompositions. J. Combin. Theory Ser. B 93, 67–72 (2005).

Colbourn C.J., Hamm R.C., Rosa A.: Embedding, immersing, and enclosing. In: Proceedings of the Sixteenth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congressus Numerantium, vol. 47, pp. 229–236. Boca Raton (1985).

Doyen J., Wilson R.M.: Embeddings of Steiner triple systems. Discret. Math. 5, 229–239 (1973).

10.

Fu H.L., Rodger C.A.: Group divisible designs with two associate classes: \(n=2\) or \(m=2\). J. Comb. Theory Ser. A 83, 94–117 (1998).

11.

Lindner C.C., Rodger C.A.: Design Theory. CRC Press, Boca Raton (1997).

12.

Newman N.A., Rodger C.A.: Enclosings of \(\lambda \)-fold 4-cycle systems. Des. Codes Cryptogr. 55, 297–310 (2010).

13.

Newman N.A., Rodger C.A.: Enclosings of \(\lambda \)-fold triple systems. Util. Math. (in press).

14.

Raines M.E., Szaniszló Z.: Equitable partial cycle systems. Australas. J. Comb. 19, 149–156 (1999).

15.

Sotteau D.: Decompositions of \(K_{m, n}(K_{m, n}^{*})\) into cycles of length \(2k\). J. Comb. Theory Ser. B 30, 75–81 (1981).

16.

West D.B.: Introduction to Graph Theory. Prentice Hall, Upper Saddle River (2001).

Titel: 4-Cycle decompositions of
verfasst von: N. A. Newman
Publikationsdatum: 01.05.2015
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 2/2015
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-013-9904-6

Springer Professional

4-Cycle decompositions of \(( \lambda +m)K_{v+u} {\setminus } \lambda K_v\)

Abstract

Premium Partner

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Weitere Artikel der Ausgabe 2/2015

Point compression for the trace zero subgroup over a small degree extension field

One-point Klein codes and their serial-in-serial-out systematic encoding

Functions which are PN on infinitely many extensions of odd

The weight distribution of a family of -ary cyclic codes

On affine sub-families of the NFSR in Grain

On the construction of Griesmer codes of dimension 5

Premium Partner