On spanning tree congestion of Hamming graphs

We present a tight lower bound for the spanning tree congestion of Hamming graphs.

💡 Research Summary

The paper investigates the spanning‑tree congestion (stc) of d‑dimensional Hamming graphs Kⁿ_d, where the vertex set consists of all d‑tuples over {0,…,n‑1} and two vertices are adjacent if they differ in exactly one coordinate. For a connected graph G, the congestion of an edge e in a spanning tree T is defined as the number of edges crossing the cut induced by removing e from T; the congestion of T is the maximum such value over all edges of T, and stc(G) is the minimum congestion over all spanning trees of G.

The authors first recall standard notation (V(G), E(G), induced subgraph G