Refining the graph density condition for the existence of almost \(K\)-factors (Q2761012)
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scientific article; zbMATH DE number 1682823
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Refining the graph density condition for the existence of almost \(K\)-factors |
scientific article; zbMATH DE number 1682823 |
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17 December 2001
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\(K\)-factors
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dense graphs
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Refining the graph density condition for the existence of almost \(K\)-factors (English)
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The paper presents an extension of a result by N. Alon and R. Yuster on finding almost \(K\)-factors in large dense graphs [Graphs Comb. 8, No. 2, 95-102 (1992; Zbl 0769.05072)] in the following sense: for \(a \leq b\) and \(\varepsilon > 0\) there exists \(N\) such that each graph \(G\) on \(n>N\) vertices and minimum degree at least \(a/(a+b)\) contains at least \((1-\varepsilon)n/(a+b)\) vertex disjoint copies of the complete bipartite graph \(K_{a,b}\). The authors conjecture that a similar result is valid for general graphs \(K\) with bounded chromatic number.
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