Has anyone seen a NP graph problem like this before?

I have a following graph-based problem:

• Input: positive integers K and L, undirected graph G

• I have to choose K vertices from this graph

• In the path between each pair of chosen K vertices there has to be at least L vertices, i. e. there has to be a "space between" each two of chosen vertices made of at least L vertices.

The above of course may not be possible for a given instance of a problem, then I have to check that. I'm quite sure that this problem is NP or even NP-complete, since it has to do with paths with length constraint. Have you ever met a similar problem? Do you have an idea how to reduce it to some more well-known problem, possibly NP, e. g. vertex cover or graph coloring?

Also, note that my graph is a grid graph, which might not be "full" but a subgraph of a full rectangular grid.

This is known as the distance-$d$ independent set, i.e., you are looking for an independent set of size $k$ where the distance between every two elements in the solution is at least $d$.

The problem is NP-complete even on planar graphs according to [1], but I don't know about its complexity on partial grids.

Regarding reductions, you can probably take the $d$'th power of the graph and find a (distance-1) independent set in that. The claim is that any solution here is a distance-$d$ independent set in the original, but you need to verify this.

[1] Eto, Hiroshi, Fengrui Guo, and Eiji Miyano. "Distance-$d$ independent set problems for bipartite and chordal graphs." Journal of Combinatorial Optimization 27, no. 1 (2014): 88-99.

StackExchange Computer Science Q#124336, answer score: 5