On Coupon Colorings of Graphs
Bob Chen, Jeong Han Kim, Michael Tait, and Jacques Verstraete

TL;DR
This paper investigates the coupon coloring number of graphs, establishing asymptotic bounds for $d$-regular graphs and showing most such graphs have a coupon coloring number close to $d/ ext{log} d$ as the number of vertices grows.
Contribution
It proves that the coupon coloring number of large $d$-regular graphs is asymptotically at least $(1 - o(1))d/ ext{log} d$ and that most such graphs have this number close to this bound.
Findings
$oxed{ ext{Coupon coloring number} ext{ of } d ext{-regular graphs} ext{ is at least } (1 - o(1))d/ ext{log} d$.
Most large $d$-regular graphs have a coupon coloring number at most $(1 + o(1))d/ ext{log} d$.
Abstract
Let be a graph with no isolated vertices. A {\em -coupon coloring} of is an assignment of colors from to the vertices of such that the neighborhood of every vertex of contains vertices of all colors from . The maximum for which a -coupon coloring exists is called the {\em coupon coloring number} of , and is denoted . In this paper, we prove that every -regular graph has as , and the proportion of -regular graphs for which tends to as .
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · graph theory and CDMA systems
