Edge-connectivity and pairwise disjoint perfect matchings in regular graphs (Q6548022)
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scientific article; zbMATH DE number 7857938
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Edge-connectivity and pairwise disjoint perfect matchings in regular graphs |
scientific article; zbMATH DE number 7857938 |
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Edge-connectivity and pairwise disjoint perfect matchings in regular graphs (English)
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31 May 2024
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Consider regular graphs which may have parallel edges but no loops. If a graph has a set of \(k\) pairwise disjoint perfect matchings we say that it has a \(k\)-PDPM. For \(0 \leq t \leq r\), Let \(m(t,r)\) be the maximum number \(s\) such that every \(t\)-edge-connected \(r\)-graph has an \(s\)-PDPM. The authors improve upper bounds for \(m(t,r)\) by establishing that \(m(2l,r) \leq 3 l - 6\) for every \(l \geq 3\) and \(r \geq 2 l\).
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perfect matchings
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regular graphs
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factors
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\(r\)-graphs
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edge-colorings
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class 2 graphs
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