Discussiones Mathematicae Graph Theory 30(1) (2010) 95-103
doi: 10.7151/dmgt.1479

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Sylwia Cichacz  and  Jakub Przybyło

AGH University of Science and Technology
Al. Mickiewicza 30, 30-059 Kraków, Poland
e-mail: przybylo@wms.mat.agh.edu.pl


In the PhD thesis by Burris (Memphis (1993)), a conjecture was made concerning the number of colors c(G) required to edge-color a simple graph G so that no two distinct vertices are incident to the same multiset of colors. We find the exact value of c(G) - the irregular coloring number, and hence verify the conjecture when G is a vertex-disjoint union of paths. We also investigate the point-distinguishing chromatic index, χ0(G), where sets, instead of multisets, are required to be distinct, and determine its value for the same family of graphs.

Keywords: irregular edge-coloring, vertex-distinguishing edge-coloring, point-distinguishing chromatic index.

2010 Mathematics Subject Classification: 05C15.


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Received 12 May 2008
Revised 3 April 2009
Accepted 3 April 2009