Graph decompositions, handcuffed prisoners and balanced P-designs
نویسندگان
چکیده
منابع مشابه
Blocking sets in handcuffed designs
In this paper we determine the spectrum of possible cardinalities of a blocking set in a H(v,3,A) and in a H(v,4,1). Moreover we construct, for each admissible ~9, a H(v,3,1) without blocking sets. Introduction A handcuffed design with parameters v, k, A, or for short an H(v,k,A), consists of a set of ordered k-subsets of a v-set, called handcuffed blocks. In a block (a., a z ' ... ,a!:) each e...
متن کاملEmbedding handcuffed designs in D-designs,
Let D be the triangle with attached edge (i. e. D is the graph having vertices {a0, a1, a2, a3} and edges {a0, a1}, {a0, a2}, {a1, a2}, {a0, a3}). J.C. Bermond and J. Schönheim [1], proved that a D-design of order n exists if and only if n ≡ 0 or 1 (mod 8). Let (W, C) be a nontrivial D-design of order n, n ≥ 8, and let V ⊂ W , |V | = v < n. We say that a handcuffed design (V,P) of order v and b...
متن کاملEmbedding handcuffed designs with block size
Let (W, C) be an m-cycle system of order n and let Ω ⊂ W , |Ω| = v < n. We say that a handcuffed design (Ω,P) of order v and block size s (2 ≤ s ≤ m−1) is contained in (W, C) if for every p ∈ P there is an m-cycle c = (a1, a2, . . . , am) ∈ C such that: (1) p = [ak, ak+1, . . . , ak+s−1] for some k ∈ {1, 2, . . . ,m} (i.e. the (s− 1)-path p occurs in the m-cycle c); and (2) ak−1, ak+s ∈ Ω. Note...
متن کاملTheta Graph Designs
We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges.
متن کاملEmbedding handcuffed designs into a maximum packing of the complete graph with 4-cycles
A packing of Kn with copies of C4 (the cycle of length 4), is an ordered triple (V, C, L), where V is the vertex set of the complete graph Kn, C is a collection of edge-disjoint copies of C4, and L is the set of edges not belonging to a block of C. The number n is called the order of the packing and the set of unused edges L is called the leave. If C is as large as possible, then (V, C, L) is c...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1972
ISSN: 0012-365X
DOI: 10.1016/0012-365x(72)90005-2