Some Locally Kneser Graphs - Brouwer, Andries (The Electronic Journal of Combinatorics, 2024)
The Kneser graph K(n,d) is the graph on the d-subsets of an n-set, adjacent when disjoint. Clearly, K(n+d,d) is locally K(n,d). Hall showed for n 3d+1 that there are no further examples. Here we give other examples of locally K(n,d) graphs for n = 3d, and some further sporadic examples. It follows that Hall’s bound is best possible.