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On colour-blind distinguishing colour pallets in regular graphs

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  • Jakub Przybyło

    (AGH University of Science and Technology)

Abstract

Consider a graph $$G=(V,E)$$ and a colouring of its edges with $$k$$ colours. Then every vertex $$v\in V$$ is associated with a ‘pallet’ of incident colours together with their frequencies, which sum up to the degree of $$v$$ . We say that two vertices have distinct pallets if they differ in frequency of at least one colour. This is always the case if these vertices have distinct degrees. We consider an apparently the worse case, when $$G$$ is regular. Suppose further that this coloured graph is being examined by a person who cannot name any given colour, but distinguishes one from another. Could we colour the edges of $$G$$ so that a person suffering from such colour-blindness is certain that colour pallets of every two adjacent vertices are distinct? Using the Lopsided Lovász Local Lemma, we prove that it is possible using 15 colours for every $$d$$ -regular graph with $$d\ge 960$$ .

Suggested Citation

  • Jakub Przybyło, 2014. "On colour-blind distinguishing colour pallets in regular graphs," Journal of Combinatorial Optimization, Springer, vol. 28(2), pages 348-357, August.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:2:d:10.1007_s10878-012-9556-x
    DOI: 10.1007/s10878-012-9556-x
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