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Let G be a graph with no isolated vertices. A k-coupon coloring of G is an assignment of colors from [k]≔{1,2,…,k} to the vertices of G such that the neighborhood of every vertex of G contains vertices of all colors from [k]. The maximum k for which a k-coupon coloring exists is called the coupon coloring number of G, and is denoted χc(G). In this paper, we prove that every d-regular graph G has χc(G)≥(1−o(1))d/logd...
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