Majority Colourings of Digraphs
We prove that every digraph has a vertex 4-colouring such that for each vertex $v$, at most half the out-neighbours of $v$ receive the same colour as $v$. We then obtain several results related to the conjecture obtained by replacing 4 by 3.
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| Veröffentlicht in: | The Electronic journal of combinatorics 2017-05, Vol.24 (2) |
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| Hauptverfasser: | , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We prove that every digraph has a vertex 4-colouring such that for each vertex $v$, at most half the out-neighbours of $v$ receive the same colour as $v$. We then obtain several results related to the conjecture obtained by replacing 4 by 3. |
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| ISSN: | 1077-8926 1077-8926 |
| DOI: | 10.37236/6410 |