Partitioning the edges of a graph |
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| Authors: | A.J.W Hilton Rhys Price Jones |
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| Affiliation: | Mathematics Dept., University of Reading, Reading, England;Mathematics Dept., Royal Holloway College, (University of London), Egham Hill, Egham, Surrey, England |
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| Abstract: | For any integer m (≥2), it is known that there are simple graphs of maximum valence m whose edges cannot be coloured with m colours in such a way that adjacent edges shall have different colours. We find those values of m and k for which it is true that every simple graph whose maximum valence does not exceed mk can be coloured with m colours in such a way that no colour appears more than k times at any vertex. |
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