A degree condition for \(k\)-uniform graphs (Q2839736)
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scientific article; zbMATH DE number 6187636
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A degree condition for \(k\)-uniform graphs |
scientific article; zbMATH DE number 6187636 |
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12 July 2013
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degree condition
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connected \([k,k+1]\)-factor
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prescribed properties
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A degree condition for \(k\)-uniform graphs (English)
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Let \(k\geq2\) be a positive integer and \(G\) be a graph of order \(n\geq4k+8\) with \(\delta(G)>k+1\) and \(kn\) even. Suppose \(\max\{d_G(x), d_G(y)\}> n\div2\) for any nonadjacent vertices \(x\) and \(y\) of \(V(G)\). The author proves that \(G\) is \(k\)-uniform. This theorem implies that \(G\) has a connected \([k,k+1]\)-factor excluding any given edge \(e\).
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