An existence theory for loopy graph decompositions
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Bibliographic record
Abstract
Let v≥k≥1 and λ≥0 be integers. Recall that a (v, k, λ) block design is a collection ℬ︁of k-subsets of a v-set X in which every unordered pair of elements in X is contained in exactly λ of the subsets in ℬ︁. Now let G be a graph with no multiple edges. A (v, G, λ) graph design is a collection ℋ︁of subgraphs, each isomoprhic to G, of the complete graph Kv such that each edge of Kv appears in exactly λof the subgraphs in ℋ︁. A famous result of Wilson states that for a fixed simple graph G and integer λ, there exists a (v, G, λ) graph design for all sufficiently large integers v satisfying certain necessary conditions. Here, we extend this result to include the case of loops in G. As a consequence, we obtain the asymptotic existence of equireplicate graph designs. Applications of the equireplicate condition are given. Copyright © 2011 Wiley Periodicals, Inc. J Combin Designs 19:280-289, 2011
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
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| Science and technology studies | 0.000 | 0.000 |
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| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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