Abstract: | In connection with his solution of the Sensitivity Conjecture, Hao Huang (arXiv: 1907.00847, 2019) asked the following question: Given a graph with high symmetry, what can we say about the smallest maximum degree of induced subgraphs of with vertices, where denotes the size of the largest independent set in ? We study this question for , the ‐dimensional Hamming graph over an alphabet of size . Generalizing a construction by Chung et al. (JCT‐A, 1988), we prove that has an induced subgraph with more than vertices and maximum degree at most . Chung et al. proved this statement for (the ‐dimensional cube). |