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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 nd the exact value of c(G) | the irregular coloring number, and hence verify the conjecture when G is a vertexdisjoint union of paths. We also investigate the point-distinguishing chromatic index, 0(G), where sets, instead of multisets, are required to be distinct, and determine its value for the same family of graphs.

Vertex-distinguishing edge-colorings of linear forests