Retracts of infinite Hamming graphs (Q1386474)

A Hamming graph is a Cartesian product of complete graphs. We show that (finite or infinite) quasi-median graphs, which are a generalization of median graphs, are exactly the retracts of Hamming graphs. This generalizes a result of \textit{H. J. Bandelt} [J. Graph Theory 8, 501-510 (1984; Zbl 0551.05060)] about median graphs, and improves a result of \textit{E. Wilkeit} [Discrete Math. 102, No. 2, 191-218 (1992; Zbl 0759.05085)] and of \textit{F. R. K. Chung}, \textit{R. L. Graham} and \textit{M. E. Saks} [Combinatorica 9, No. 2, 111-131 (1989; Zbl 0692.05055)] about finite quasi-median graphs.