Abstract
Let Q n be a hypercube of dimension n, that is, a graph whose vertices are binary n-tuples and two vertices are adjacent iff the corresponding n-tuples differ in exactly one position. An edge coloring of a graph H is called rainbow if no two edges of H have the same color. Let f(G,H) be the largest number of colors such that there exists an edge coloring of G with f(G,H) colors such that no subgraph isomorphic to H is rainbow. In this paper we start the investigation of this anti-Ramsey problem by providing bounds on f(Q n ,Q k ) which are asymptotically tight for k = 2 and by giving some exact results.
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Axenovich, M., Harborth, H., Kemnitz, A. et al. Rainbows in the Hypercube. Graphs and Combinatorics 23, 123–133 (2007). https://doi.org/10.1007/s00373-007-0691-6
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DOI: https://doi.org/10.1007/s00373-007-0691-6