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Gap vertex-distinguishing edge colorings of graphs

✍ Scribed by M.A. Tahraoui; E. Duchêne; H. Kheddouci

Book ID
116410137
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
457 KB
Volume
312
Category
Article
ISSN
0012-365X

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We prove the conjecture of Burris and Schelp: a coloring of the edges of a graph of order n such that a vertex is not incident with two edges of the same color and any two vertices are incident with different sets of colors is possible using at most n+1 colors. 1999 Academic Press ## 1. Introducti

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An edge-coloring is called vertex-distinguishing if every two distinct vertices are incident to different sets of colored edges. The minimum number of colors required for a vertex-distinguishing proper edge-coloring of a simple graph G is denoted by χ s (G). A simple count shows that χ s (G) ≥ max{(