\(P_3\)-factorization of complete multipartite graphs (Q1288299)
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scientific article; zbMATH DE number 1286446
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(P_3\)-factorization of complete multipartite graphs |
scientific article; zbMATH DE number 1286446 |
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\(P_3\)-factorization of complete multipartite graphs (English)
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15 September 1999
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The author provides necessary and sufficient conditions for the existence of a \(P_3\)-factorization of the complete multipartite graph \(\lambda K^n_m\). Namely he proves such conditions are (i) \(m\geq 3\), (ii) \(mn\equiv 0\pmod 3\), and (iii) \(\lambda(m-1)n\equiv 0\pmod 4\). The proof is by construction and uses suitable resolvable group divisible designs with an even number of resolution classes.
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complete multipartite graph
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