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Vertex-distinguishing edge-colorings of linear forests
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 1, pp. 95-103 Cet article a éte moissonné depuis la source Library of Science

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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 
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Cichacz, Sylwia; Przybyło, Jakub. Vertex-distinguishing edge-colorings of linear forests. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 1, pp. 95-103. http://geodesic.mathdoc.fr/item/DMGT_2010_30_1_a7/

[1] M. Aigner and E. Triesch, Irregular assignments and two problems á la Ringel, in: Topics in Combinatorics and Graph Theory, dedicated to G. Ringel, Bodendiek, Henn, eds. (Physica Verlag Heidelberg, 1990) 29-36.

[2] P.N. Balister, Packing Circuits into Kₙ, Combin. Probab. Comput. 10 (2001) 463-499, doi: 10.1017/S0963548301004771.

[3] P.N. Balister, B. Bollobás and R.H. Schelp, Vertex-distinguishing edge-colorings of graphs with Δ(G) = 2, Discrete Math. 252 (2002) 17-29, doi: 10.1016/S0012-365X(01)00287-4.

[4] A.C. Burris, Vertex-distinguishing edge-colorings (PhD Thesis, Memphis, 1993).

[5] A.C. Burris and R.H. Schelp, Vertex-distiguishing proper edge-colorings, J. Graph Theory 26 (1997) 73-82, doi: 10.1002/(SICI)1097-0118(199710)26:273::AID-JGT2>3.0.CO;2-C

[6] J. Cerný, M. Hornák and R. Soták, Observability of a graph, Math. Slovaca 46 (1996) 21-31.

[7] G. Chartrand, M.S. Jacobson, J. Lehel, O.R. Oellermann, S. Ruiz and F. Saba, Irregular Networks, Congressus Numerantium 64 (1988) 187-192.

[8] S. Cichacz, J. Przybyło and M. Woźniak, Decompositions of pseudographs into closed trails of even sizes, Discrete Math. 309 (2009) 4903-4908, doi: 10.1016/j.disc.2008.04.024.

[9] S. Cichacz, J. Przybyło and M. Woźniak, Irregular edge-colorings of sums of cycles of even lengths, Australas. J. Combin. 40 (2008) 41-56.

[10] F. Harary and M. Plantholt, The point-distinguishing chromatic index, in: Graphs and Applications, Proc. 1st Symp. Graph Theory, Boulder/Colo. 1982, (1985) 147-162.