Plane graphs are entirely \((\Delta + 5)\)-choosable (Q2875688)
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scientific article; zbMATH DE number 6328440
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Plane graphs are entirely \((\Delta + 5)\)-choosable |
scientific article; zbMATH DE number 6328440 |
Statements
11 August 2014
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plane graph
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entire choosability
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maximum degree
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discharging method
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Plane graphs are entirely \((\Delta + 5)\)-choosable (English)
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Assume that we assign a list of colors \(L(x)\), \(|L(x)|\leq k\), to each element \(x\) of the set \(V(G)\cup E(G)\cup F(G)\), where \(G\) is a plane graph. If it is possible to color the elements of \(V(G)\cup E(G)\cup F(G)\) in such a way that all the adjacent and incident elements have distinct colors, then we say that \(G\) is entirely \(k\)-choosable. The authors use the discharching method to show that every plane graph with \(\Delta(G)\leq 5\) is entirely \((\Delta(G)+5)\)-choosable.
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