Abstract

ABSTRACTThe anti‐Ramsey number of an ‐graph is the minimum number of colors needed to color the complete ‐vertex ‐graph to ensure the existence of a rainbow copy of . We establish a removal‐type result for the anti‐Ramsey problem of when is the expansion of a hypergraph with a smaller uniformity. We present two applications of this result. First, we refine the general bound proved by Erdős–Simonovits–Sós, where denotes the family of ‐graphs obtained from by removing one edge. Second, we determine the exact value of for large in cases where is the expansion of a specific class of graphs. This extends results of Erdős–Simonovits–Sós on complete graphs to the realm of hypergraphs.

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