Abstract The Kneser cube Knₙ K n n has vertex set 2^n 2 n and two vertices F, F' F, F ′ are joined by an edge if and only if F F'= F ∩ F ′ = ∅. For a fixed graph G, we are interested in the most number vex (n, G) vex (n, G) of vertices of Knₙ K n n that span a G -free subgraph in Knₙ K n n. We show that the asymptotics of vex (n, G) vex (n, G) is (1+o (1) ) 2^n-1 (1 + o (1) ) 2 n - 1 for bipartite G and (1-o (1) ) 2ⁿ (1 - o (1) ) 2 n for graphs with chromatic number at least 3. We also obtain results on the order of magnitude of 2^n-1-\!vex (n, G) 2 n - 1 - vex (n, <mm
Gerbner et al. (2026) studied this question.