The spectrum of α-resolvable λ-fold (K_4 - e)-designs (original) (raw)
2016, Ars Mathematica Contemporanea
Related papers
Contributions Discret. Math., 2017
A λ-fold G-design is said to be α-resolvable if its blocks can be partitioned into classes such that every class contains each vertex exactly α times. In this paper we study the existence problem of an α-resolvable λ-fold G-design oforder v in the case when G is any connected subgraph of K_4 and prove that the necessary conditions for its existence are also sufficient.
Two types of switchable λ-fold (K4−e)-designs
Discrete Mathematics, 2008
In this paper the existence of two types of edge-switchable (K 4 − e, λ)-designs are investigated. It is established that the necessary conditions for a Type I switchable (λK v , K 4 − e)-design is λ(v − 1) ≡ 0 (mod 5), v ≥ 4, and these conditions are also sufficient except for (v, λ) = (11, 1). The necessary conditions for a Type II switchable (λK v , K 4 − e)-design are λv(v − 1) ≡ 0 (mod 10), v ≥ 4, and these conditions are also sufficient with a small number of possible exceptions.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.