Union vertex-distinguishing edge colorings

03/05/2023

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by   Teeradej Kittipassorn, et al.

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The union vertex-distinguishing chromatic index χ'_∪(G) of a graph G is the smallest natural number k such that the edges of G can be assigned nonempty subsets of [k] so that the union of the subsets assigned to the edges incident to each vertex is different. We prove that χ'_∪(G) ∈{⌈log_2(n +1) ⌉, ⌈log_2(n +1) ⌉+1 } for a graph G on n vertices without a component of order at most two. This answers a question posed by Bousquet, Dailly, Duchêne, Kheddouci and Parreau, and independently by Chartrand, Hallas and Zhang.