A note on restricted list edge-colourings (Q1715081)
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scientific article; zbMATH DE number 7011214
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on restricted list edge-colourings |
scientific article; zbMATH DE number 7011214 |
Statements
A note on restricted list edge-colourings (English)
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1 February 2019
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By extending the method of \textit{F. Galvin} [J. Comb. Theory, Ser. B 63, No. 1, 153--158 (1995; Zbl 0826.05026)] and using the stable marriage theorem of \textit{D. Gale} and \textit{L. S. Shapley} [Am. Math. Mon. 69, 9--15 (1962; Zbl 0109.24403)], the author proves an extension of Galvin's theorem, namely that any graph is $L$-edge-choosable if $\vert L(e)\vert \geq \chi '(G)$ and the edge-lists of no odd cycle contain a common colour.
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restricted list edge-colourings
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$L$-edge-choosable graph
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odd cycle
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stable matching
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Galvin's theorem
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Gale-Shapley's theorem
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