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- W2949271658 abstract "Let $G$ be a graph with no isolated vertices. A {em $k$-coupon coloring} of $G$ is an assignment of colors from $[k] := {1,2,dots,k}$ 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 {em coupon coloring number} of $G$, and is denoted $chi_{c}(G)$. In this paper, we prove that every $d$-regular graph $G$ has $chi_{c}(G) geq (1 - o(1))d/log d$ as $d rightarrow infty$, and the proportion of $d$-regular graphs $G$ for which $chi_c(G) leq (1 + o(1))d/log d$ tends to $1$ as $|V(G)| rightarrow infty$." @default.
- W2949271658 created "2019-06-27" @default.
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- W2949271658 date "2014-04-24" @default.
- W2949271658 modified "2023-10-14" @default.
- W2949271658 title "On Coupon Colorings of Graphs" @default.
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- W2949271658 doi "https://doi.org/10.48550/arxiv.1404.6278" @default.
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