On colour-blind distinguishing colour pallets in regular graphs

Jakub Przybyło ()
Additional contact information
Jakub Przybyło: AGH University of Science and Technology

Journal of Combinatorial Optimization, 2014, vol. 28, issue 2, No 3, 348-357

Abstract: 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 $$d\ge 960$$ .

Keywords: Neighbour-distinguishing colouring; Lopsided Lovász Local Lemma; Colour pallet (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-012-9556-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:28:y:2014:i:2:d:10.1007_s10878-012-9556-x

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-012-9556-x

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().