List Colouring Squares of Planar Graphs
In 1977, Wegner conjectured that the chromatic number of the square of every planar graph $G$ with maximum degree $\Delta\ge8$ is at most $\lfloor\frac32 \Delta\bigr+1$. We show that it is at most $\frac32 \Delta (1+o(1))$, and indeed this is true for the list chromatic number and for more general c...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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2008
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| _version_ | 1826278877610115072 |
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| author | Havet, F Heuvel, J McDiarmid, C Reed, B |
| author_facet | Havet, F Heuvel, J McDiarmid, C Reed, B |
| author_sort | Havet, F |
| collection | OXFORD |
| description | In 1977, Wegner conjectured that the chromatic number of the square of every planar graph $G$ with maximum degree $\Delta\ge8$ is at most $\lfloor\frac32 \Delta\bigr+1$. We show that it is at most $\frac32 \Delta (1+o(1))$, and indeed this is true for the list chromatic number and for more general classes of graphs. |
| first_indexed | 2024-03-06T23:50:31Z |
| format | Journal article |
| id | oxford-uuid:72700038-1786-400c-867b-8aaac74ddb3c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:50:31Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | oxford-uuid:72700038-1786-400c-867b-8aaac74ddb3c2022-03-26T19:50:03ZList Colouring Squares of Planar GraphsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:72700038-1786-400c-867b-8aaac74ddb3cEnglishSymplectic Elements at Oxford2008Havet, FHeuvel, JMcDiarmid, CReed, BIn 1977, Wegner conjectured that the chromatic number of the square of every planar graph $G$ with maximum degree $\Delta\ge8$ is at most $\lfloor\frac32 \Delta\bigr+1$. We show that it is at most $\frac32 \Delta (1+o(1))$, and indeed this is true for the list chromatic number and for more general classes of graphs. |
| spellingShingle | Havet, F Heuvel, J McDiarmid, C Reed, B List Colouring Squares of Planar Graphs |
| title | List Colouring Squares of Planar Graphs |
| title_full | List Colouring Squares of Planar Graphs |
| title_fullStr | List Colouring Squares of Planar Graphs |
| title_full_unstemmed | List Colouring Squares of Planar Graphs |
| title_short | List Colouring Squares of Planar Graphs |
| title_sort | list colouring squares of planar graphs |
| work_keys_str_mv | AT havetf listcolouringsquaresofplanargraphs AT heuvelj listcolouringsquaresofplanargraphs AT mcdiarmidc listcolouringsquaresofplanargraphs AT reedb listcolouringsquaresofplanargraphs |