On the existence of a matching orthogonal to a 2-factorization (Q1262879)
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scientific article; zbMATH DE number 4125437
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the existence of a matching orthogonal to a 2-factorization |
scientific article; zbMATH DE number 4125437 |
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On the existence of a matching orthogonal to a 2-factorization (English)
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1989
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Brian Alspach in 1988 posed the following problem: For any 2- factorization \(F_ 1,F_ 2,...,F_ d\) of a 2d-regular graph G, is it possible to find a d-matching M in G such that M contains precisely one edge from each of \(F_ 1,F_ 2,...,F_ d?\) The authors of this article show that if \(F_ 1,F_ 2,...,F_ d\) is a 2-factorization of a 2d- regular graph G of order \(n\geq 3,23d\), then G contains a d-matching with exactly one edge from each of \(F_ 1,F_ 2,...,F_ d\).
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2-factorization
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2d-regular graph
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d-matching
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