On the cyclic decomposition of complete graphs into almost-bipartite graphs

Blinco, Andrew; El-Zanati, Saad I.; Eynden, Charles Vanden

doi:10.1016/j.disc.2003.11.024

Cited by 29 publications

(41 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also have the following three results. Theorem 5.5 was proved by Blinco and El-Zanati [33], and Theorem 5.6 was proved by Aguado et al [19], both being obtained under the guise of graph labelings. The first part of Theorem 5.7 is proven by Dinitz and Rodney [56] (using graph labelings) while the second part is established by Horak and Rosa [77].…”

Section: Even Graphsmentioning

confidence: 85%

A survey on the existence ofG‐Designs

Adams

Bryant

Buchanan

2007

J of Combinatorial Designs

196

View full text Add to dashboard Cite

show abstract

Section: Even Graphsmentioning

confidence: 85%

A survey on the existence ofG‐Designs

Adams

Bryant

Buchanan

2007

J of Combinatorial Designs

196

View full text Add to dashboard Cite

show abstract

“…[3] and, independently, in [5,6,10]. The same has been done for cyclic k-cycle systems of the complete m-partite graph K mÂk with m and k odd (see Ref.…”

Section: Introductionmentioning

confidence: 98%

Cyclic k‐cycle systems of order 2kn + k: A solution of the last open cases

Vietri¹

2004

J of Combinatorial Designs

View full text Add to dashboard Cite

We exhibit cyclic ðK v v ; C k Þ-designs with v v > k; v v k ðmod 2kÞ, for k an odd prime power but not a prime, and for k ¼ 15. Such values were the only ones not to be analyzed yet, under the hypothesis v v k (mod 2kÞ: Our construction avails of Rosa sequences and approximates the Hamiltonian case ðv v ¼ kÞ; which is known to admit no cyclic design with the same values of k: As a particular consequence, we settle the existence question for cyclic ðK v v ; C k Þ-designs with k a prime power. #

show abstract

“…The existence problem for a cyclic k-cycle system of K v has been solved, with the contribution of many authors ( [10,11,14,16,[18][19][20]23]), in the case of v ≡ 1 or k (mod 2k) (see also [2,4,12]). In all other cases it is conjectured (see [9,24]) that a cyclic k-cycle system of K v exists for any admissible pair (k, v) provided v>2k whenever gcd(k, v) is a prime power.…”

Section: Introductionmentioning

confidence: 99%