Abstract
Recently the generalized Doyen-Wilson problem of embedding a 5-cycle system of order u in one of order υ was completely solved. However it is often useful to solve the more general problem of the existence of a 5-cycle system of order υ with a hole of size u. In this paper we completely solve this problem.
Research supported by NSF grant DMS 9225046
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. E. Bryant and C. A. Rodger, On the Doyen-Wilson Theorem for m-cycle systems, J. Combin. Designs, Vol. 2 (1994) pp. 253–271.
D. E. Bryant and C. A. Rodger, The Doyen-Wilson Theorem extended to 5-cycles, J. Combin. Theory Ser. A, Vol. 68 (1994) pp. 218–224.
J. Doyen and R. M. Wilson, Embeddings of Steiner triple systems, Discrete Math, Vol. 5 (1973) pp. 229–239.
D. G. Hoffman and C. A. Rodger, The chromatic index of complete multipartite graphs, J. Graph Theory, Vol. 16 (1992) pp. 159–163.
C. A. Rodger, Problems on cycle systems of odd length, Cong. Numer., Vol. 61 (1988) pp. 5–22.
E. Mendelsohn and A. Rosa, Embedding maximum packings of triples, Cong. Numer., Vol. 40 (1983) pp. 235–247.
G. Stern and A. Lenz, Steiner triple systems with given subspaces; another proof of the Doyen-Wilson theorem, Boll. Un. Mat. Ital. A (5), Vol. 17 (1980) pp. 109–114.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Dedicated to Hanfried Lenz on the occasion of his 80th birthday
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers, Boston
About this chapter
Cite this chapter
Bryant, D.E., Hoffman, D.G., Rodger, C.A. (1996). 5-Cycle Systems with Holes. In: Jungnickel, D. (eds) Designs and Finite Geometries. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1395-3_7
Download citation
DOI: https://doi.org/10.1007/978-1-4613-1395-3_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-8604-2
Online ISBN: 978-1-4613-1395-3
eBook Packages: Springer Book Archive